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Log 4 – (log 3 – log 4)= log 3 – log 5 + log 5 – log 4 – log 3 + log 4= 0(ii) 3x+y-z3x+y-z = 30= 1Question 9. If x = log10 12, y = log4 2 × log10 9 and z = log10 0.4, find the values of(i) x – y – z(ii) 7x-y-zAnswer:Given:x = log10 12y = log4 2 × log10 9z = log10 0.4(i) x – y – zLet us substitute the given values, we getx – y – z = log10 12 – log4 2 × log10 9 – log10 0.4= log10 (3×4) – log4 41/2 × log10 32 – log10 4/10= log10 3 + log10 4 – ½ log4 4 × 2 log10 3 – (log10 4 – log10 10)= log10 3 + log10 4 – ½ × 1 × 2 log10 3 – log10 4 + 1= log10 3 + log10 4 – log10 3 – log10 4 + 1= 1(ii) 7x-y-z7x-y-z = 71= 7Question 10. If log V + log 3 = log π + log 4 + 3 log r, find V in terms of other quantities.Answer:Given:log V + log 3 = log π + log 4 + 3 log rLet us simplify the given expression to find V,log (V × 3) = log (π × 4 × r3)log 3V = log 4πr33V = 4πr3V = 4πr3/3Question 11. Given 3 (log 5 – log 3) – (log 5 – 2 log 6) = 2 – log n, find n.Answer:Given:3 (log 5 – log 3) – (log 5 – 2 log 6) = 2 – log nLet us simplify the given expression to find n,3 log 5 – 3 log 3 – log 5 + 2 log 6 = 2 – log n2 log 5 – 3 log 3 + 2 log 6 = 2 (1) – log nlog 52 – log 33 + log 62 = 2 log 10 – log n [Since, 1 = log 10]log 25 – log 27 + log 36 – log 102 = – log nlog n = – log 25 + log 27 – log 36 + log 100= (log 100 + log 27) – (log 25 + log 36)= log (100×27) – log (25×36)= log (100×27)/(25×36)log n = log 3n = 3Question 12. Given that log10 y + 2 log10 x = 2, express y in terms of x.Answer:Given:log10 y + 2 log10 x = 2Let us simplify the given expression,log10 y + log10 x2 = 2(1)log10 y + log10 x2 = 2 log10 10log10 (y×x2) = log10 102yx2 = 100y = 100/x2Question 13. Express log10 2 + 1 in the form log10x.Answer:Given:log10 2 + 1Let us simplify the given expression,log10 2 + 1 = log10 2 + log10 10 [Since, 1 = log10 10 ]= log10 (2×10)= log10 20Question 14. If a2 = log10 x, b2 = log10 y and a2/2 – b2/3 = log10 z. Express z in terms of x and y.Answer:Given:a2 = log10 xb2 = log10 ya2/2 –

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B2/3 = log10 zLet us substitute the given values in the expression, we getlog10 x/2 – log10 y/3 = log10 zlog10 x1/2 – log10 y1/3 = log10 zlog10 √x – log10 ∛y = log10 zlog10 √x/∛y = log10 z√x/∛y = zz = √x/∛yQuestion 15. Given that log m = x + y and log n = x – y, express the value of log m²n in terms of x and y.Answer:Given:log m = x + ylog n = x – ylog m²nLet us simplify the given expression,log m²n = log m2 + log n= 2 log m + log nBy substituting the given values, we get= 2 (x + y) + (x – y)= 2x + 2y + x – y= 3x + yQuestion 16. Given that log x = m + n and log y = m – n, express the value of log (10x/y2) in terms of m and n.Answer:Given:log x = m + nlog y = m – nlog (10x/y2)Let us simplify the given expression,log (10x/y2) = log 10x – log y2= log 10 + log x – 2 log y= 1 + log x – 2 log y= 1 + (m + n) – 2(m – n)= 1 + m + n – 2m + 2n= 1 – m + 3nQuestion 17. If log x/2 = log y/3, find the value of y4/x6.Answer:Given:log x/2 = log y/3Let us simplify the given expression,By cross multiplying, we get3 log x = 2 log ylog x3 = log y2so, x3 = y2now square on both sides, we get(x3)2 = (y2)2x6 = y4y4/x6 = 1Question 18. Solve for x:(i) log x + log 5 = 2 log 3(ii) log3 x – log3 2 = 1(iii) x = log 125/log 25(iv) (log 8/log 2) × (log 3/log√3) = 2 log xAnswer:(i) log x + log 5 = 2 log 3Let us solve for x,Log x = 2 log 3 – log 5= log 32 – log 5= log 9 – log 5= log (9/5)∴ x = 9/5(ii) log3 x – log3 2 = 1Let us solve for x,log3 x = 1 + log3 2= log3 3 + log3 2 [Since, 1 can be written as log3 3 = 1]= log3 (3×2)= log3 6∴ x = 6(iii) x = log 125/log 25x = log 53/log52= 3 log 5/ 2 log 5= 3/2 [Since, log 5/log 5 = 1]∴ x = 3/2(iv) (log 8/log 2) × (log 3/log√3) = 2 log x(log 23/log 2) × (log 3/log31/2) = 2 log x(3log 2/log 2) × (log 3/½ log 3) = 2 log x3 × 1/(½) = 2 log x3 × 2 = 2 log x6 = 2 log xlog x = 6/2log x = 3x = (10)3= 1000∴ x = 1000Question 19. Given 2 log10 x + 1= log10 250, find(i) x(ii) log102xAnswer:Given:2 log10 x + 1= log10 250(i) let us simplify the above expression,log10 x2 + log10 10 = log10 250 [Since, 1 can be written as log10 10]log10 (x2 × 10) =

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Most recent 5000 log messages (the display limit). To display User Access logs: 1.Select System > Log/Monitoring. 2.Click the User Access tab. 3.Click the Log tab. 4.Use the features described in Table to examine log records or manage the log collection. Displaying Admin Access Logs The Admin Access logs include information about administrator actions, such as administrator changes to user, system, and network settings. It includes a log entry whenever an administrator signs in, signs out, or changes licenses on the appliance. The local log viewer displays the most recent 5000 log messages (the display limit). To display Admin Access logs: 1.Select System Log/Monitoring. 2.Click the Admin Access tab. 3.Click the Log tab. 4.Use the features described in Table to examine log records or manage the log collection. Displaying Sensor Logs The Sensor logs include information related to communication with an IDP sensor if you have deployed a coordinated threat control solution. The local log viewer displays the most recent 5000 log messages (the display limit). To display Sensor logs: 1.Select System > Log/Monitoring. 2.Click the Sensor tab. 3.Click the Log tab. 4.Use the features described in Table to examine log records or manage the log collection. Using Log Filters This topic describes how to use log filters. Reviewing the Configuration of Predefined Log Format Filters To view the configuration of predefined log format filters: 1.Select System > Log/Monitoring. 2.Click the Events tab. 3.Click the Filter tab to display the log filters page. Log Filters Page - Ivanti Connect Secure. 1,289 Followers, 4,033 Following, 114 Posts - Justin Armour (@adguru) on Instagram: Log In. Sign Up Log In. Sign Up. adguru. Follow. 114 posts. 1,289 followers. 3,751 following. Justin TikTok video from @adguru Why putting all your resources into one ad platform can be a big mistake? marketingstrategy. original sound - Shad Salleh - @adguru. Log in.

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Item ID18465Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18466Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18471Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18474Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18475Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18482Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18485Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18486Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18488Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18490Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18494Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18495Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18497Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18499Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18501Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18502Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18508Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18509Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18513Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18553Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18561Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18563Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18564Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18571Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18575Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18576Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18578Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18579Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18580Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18582Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18507Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18589Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18572Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18512Format(.psd) Photoshop CS6Please

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Including log archiving. Select Events to Log - Events Tab Connection Requests Log events related to connection requests. System Status Log events related to changes in system status. Rewrite Log events related to rewrite policies. System Errors Log events related to system errors. Statistics Log user access statistics reported on the System > Log/Monitoring > Statistics tab. If you unselect the Statistics option, the statistics are not written to the log file, but are still reported on the statistics page. Performance Log events related to SiteMinder. License Protocol Events Log events related to licensing. Reverse Proxy Logs events related to reverse proxy information. Select Events to Log - User Access Tab Login/logout Log events related to sign in and sign out. SAM/Java Log events related to user access to SAM/Java in the local log file. User Settings Log events related to changes to user settings in the local log file. Meeting Events Log events related to meeting information. Client Certificate Log events related to certificate security. IF-MAP Client User Messages Log events related to IF-MAP. Pulse Client Messages Log events related to Pulse clients. HTML5 Access Log events related to HTML5 access. Web Requests Log events related to user access to web. File Requests Log events related to user access to files. Meeting Log events related to user access to meetings. Secure Terminal Log events related to user access to secure terminal. VPN Tunneling Log events related to user access to VPN tunneling. SAML Log events related to user access

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Source Virtualization tab.Select the Enable Virtualization check box.Click Create Virtual Log Sources.The Create Virtual Log Sources dialog box appears.In the Log Source Virtualization Template menu, select Open Collector - Sophos Central.Click Save.The confirmation prompt appears.Click OK.New Log Sources appear in the grid as children of your parent log source.Step 4: Apply the Log Source Virtualization Template for Sophos Central Beat Heartbeat MessagesUse the log source virtualization template included in the KB to create a log source specifically for Sophos Central heartbeat logs. This step is not required for beats configured using the JSON Parsing method that have had Long-Running LRCTL configured so that their heartbeat status can be monitored in the Beats Grid in the Web Console UI.Double-click the newly accepted Open Collector Log Source.The Log Message Source Properties window appears.Click the Log Source Virtualization tab.Select the Enable Virtualization check box.Click Create Virtual Log Sources.The Create Virtual Log Sources dialog box appears.In the Log Source Virtualization Template menu, select Open Collector - SophosCentralBeat Heartbeat.Click Save.The confirmation prompt appears.Click OK.New Log Sources appear in the grid as children of your parent log source.Step 5: (Optional) Enable Silent Log Source DetectionSilent Log Source Detection indicates when one of your log sources has stopped reporting logs.Double-click a child log source—for example, Syslog - Open Collector - Sophos Central.The Virtual Log Message Source Properties window appears.Click the Additional Settings tab.Select the Enable Silent Log Source Detection check box.Configure warning and error intervals. LogRhythm recommends warning after 1 hour and error after 2 hours. Click OK.Click the Alarm Rules tab.Search for LogRhythm Silent Log Source Error and ensure that the value in the Status column is Enabled.. 1,289 Followers, 4,033 Following, 114 Posts - Justin Armour (@adguru) on Instagram: Log In. Sign Up Log In. Sign Up. adguru. Follow. 114 posts. 1,289 followers. 3,751 following. Justin TikTok video from @adguru Why putting all your resources into one ad platform can be a big mistake? marketingstrategy. original sound - Shad Salleh - @adguru. Log in.

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Log 4 – (log 3 – log 4)= log 3 – log 5 + log 5 – log 4 – log 3 + log 4= 0(ii) 3x+y-z3x+y-z = 30= 1Question 9. If x = log10 12, y = log4 2 × log10 9 and z = log10 0.4, find the values of(i) x – y – z(ii) 7x-y-zAnswer:Given:x = log10 12y = log4 2 × log10 9z = log10 0.4(i) x – y – zLet us substitute the given values, we getx – y – z = log10 12 – log4 2 × log10 9 – log10 0.4= log10 (3×4) – log4 41/2 × log10 32 – log10 4/10= log10 3 + log10 4 – ½ log4 4 × 2 log10 3 – (log10 4 – log10 10)= log10 3 + log10 4 – ½ × 1 × 2 log10 3 – log10 4 + 1= log10 3 + log10 4 – log10 3 – log10 4 + 1= 1(ii) 7x-y-z7x-y-z = 71= 7Question 10. If log V + log 3 = log π + log 4 + 3 log r, find V in terms of other quantities.Answer:Given:log V + log 3 = log π + log 4 + 3 log rLet us simplify the given expression to find V,log (V × 3) = log (π × 4 × r3)log 3V = log 4πr33V = 4πr3V = 4πr3/3Question 11. Given 3 (log 5 – log 3) – (log 5 – 2 log 6) = 2 – log n, find n.Answer:Given:3 (log 5 – log 3) – (log 5 – 2 log 6) = 2 – log nLet us simplify the given expression to find n,3 log 5 – 3 log 3 – log 5 + 2 log 6 = 2 – log n2 log 5 – 3 log 3 + 2 log 6 = 2 (1) – log nlog 52 – log 33 + log 62 = 2 log 10 – log n [Since, 1 = log 10]log 25 – log 27 + log 36 – log 102 = – log nlog n = – log 25 + log 27 – log 36 + log 100= (log 100 + log 27) – (log 25 + log 36)= log (100×27) – log (25×36)= log (100×27)/(25×36)log n = log 3n = 3Question 12. Given that log10 y + 2 log10 x = 2, express y in terms of x.Answer:Given:log10 y + 2 log10 x = 2Let us simplify the given expression,log10 y + log10 x2 = 2(1)log10 y + log10 x2 = 2 log10 10log10 (y×x2) = log10 102yx2 = 100y = 100/x2Question 13. Express log10 2 + 1 in the form log10x.Answer:Given:log10 2 + 1Let us simplify the given expression,log10 2 + 1 = log10 2 + log10 10 [Since, 1 = log10 10 ]= log10 (2×10)= log10 20Question 14. If a2 = log10 x, b2 = log10 y and a2/2 – b2/3 = log10 z. Express z in terms of x and y.Answer:Given:a2 = log10 xb2 = log10 ya2/2 –

2025-04-02
User2744

B2/3 = log10 zLet us substitute the given values in the expression, we getlog10 x/2 – log10 y/3 = log10 zlog10 x1/2 – log10 y1/3 = log10 zlog10 √x – log10 ∛y = log10 zlog10 √x/∛y = log10 z√x/∛y = zz = √x/∛yQuestion 15. Given that log m = x + y and log n = x – y, express the value of log m²n in terms of x and y.Answer:Given:log m = x + ylog n = x – ylog m²nLet us simplify the given expression,log m²n = log m2 + log n= 2 log m + log nBy substituting the given values, we get= 2 (x + y) + (x – y)= 2x + 2y + x – y= 3x + yQuestion 16. Given that log x = m + n and log y = m – n, express the value of log (10x/y2) in terms of m and n.Answer:Given:log x = m + nlog y = m – nlog (10x/y2)Let us simplify the given expression,log (10x/y2) = log 10x – log y2= log 10 + log x – 2 log y= 1 + log x – 2 log y= 1 + (m + n) – 2(m – n)= 1 + m + n – 2m + 2n= 1 – m + 3nQuestion 17. If log x/2 = log y/3, find the value of y4/x6.Answer:Given:log x/2 = log y/3Let us simplify the given expression,By cross multiplying, we get3 log x = 2 log ylog x3 = log y2so, x3 = y2now square on both sides, we get(x3)2 = (y2)2x6 = y4y4/x6 = 1Question 18. Solve for x:(i) log x + log 5 = 2 log 3(ii) log3 x – log3 2 = 1(iii) x = log 125/log 25(iv) (log 8/log 2) × (log 3/log√3) = 2 log xAnswer:(i) log x + log 5 = 2 log 3Let us solve for x,Log x = 2 log 3 – log 5= log 32 – log 5= log 9 – log 5= log (9/5)∴ x = 9/5(ii) log3 x – log3 2 = 1Let us solve for x,log3 x = 1 + log3 2= log3 3 + log3 2 [Since, 1 can be written as log3 3 = 1]= log3 (3×2)= log3 6∴ x = 6(iii) x = log 125/log 25x = log 53/log52= 3 log 5/ 2 log 5= 3/2 [Since, log 5/log 5 = 1]∴ x = 3/2(iv) (log 8/log 2) × (log 3/log√3) = 2 log x(log 23/log 2) × (log 3/log31/2) = 2 log x(3log 2/log 2) × (log 3/½ log 3) = 2 log x3 × 1/(½) = 2 log x3 × 2 = 2 log x6 = 2 log xlog x = 6/2log x = 3x = (10)3= 1000∴ x = 1000Question 19. Given 2 log10 x + 1= log10 250, find(i) x(ii) log102xAnswer:Given:2 log10 x + 1= log10 250(i) let us simplify the above expression,log10 x2 + log10 10 = log10 250 [Since, 1 can be written as log10 10]log10 (x2 × 10) =

2025-04-21
User4282

Item ID18465Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18466Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18471Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18474Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18475Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18482Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18485Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18486Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18488Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18490Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18494Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18495Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18497Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18499Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18501Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18502Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18508Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18509Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18513Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18553Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18561Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18563Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18564Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18571Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18575Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18576Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18578Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18579Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18580Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18582Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18507Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18589Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18572Format(.psd) Photoshop CS6Please log in, in order to download or purchase credits.Item ID18512Format(.psd) Photoshop CS6Please

2025-04-07
User4159

Including log archiving. Select Events to Log - Events Tab Connection Requests Log events related to connection requests. System Status Log events related to changes in system status. Rewrite Log events related to rewrite policies. System Errors Log events related to system errors. Statistics Log user access statistics reported on the System > Log/Monitoring > Statistics tab. If you unselect the Statistics option, the statistics are not written to the log file, but are still reported on the statistics page. Performance Log events related to SiteMinder. License Protocol Events Log events related to licensing. Reverse Proxy Logs events related to reverse proxy information. Select Events to Log - User Access Tab Login/logout Log events related to sign in and sign out. SAM/Java Log events related to user access to SAM/Java in the local log file. User Settings Log events related to changes to user settings in the local log file. Meeting Events Log events related to meeting information. Client Certificate Log events related to certificate security. IF-MAP Client User Messages Log events related to IF-MAP. Pulse Client Messages Log events related to Pulse clients. HTML5 Access Log events related to HTML5 access. Web Requests Log events related to user access to web. File Requests Log events related to user access to files. Meeting Log events related to user access to meetings. Secure Terminal Log events related to user access to secure terminal. VPN Tunneling Log events related to user access to VPN tunneling. SAML Log events related to user access

2025-03-28
User3650

HomeSolarWinds Kiwi Log Viewer vs. SolarWinds Log AnalyzerSolarWinds Kiwi Log Viewer and SolarWinds Log Analyzer are both solutions in the Log Management category. SolarWinds Kiwi Log Viewer is ranked #77, while SolarWinds Log Analyzer is ranked #51. SolarWinds Kiwi Log Viewer holds a 0.0% mindshare in Log Management, compared to SolarWinds Log Analyzer’s 0.4% mindshare. Comparison Buyer's GuideWe performed a comparison between SolarWinds Kiwi Log Viewer and SolarWinds Log Analyzer based on real PeerSpot user reviews.Find out what your peers are saying about Wazuh, Splunk, Datadog and others in Log Management.To learn more, read our detailed Log Management Report (Updated: March 2025).Review summaries and opinionsCategories and RankingSolarWinds Kiwi Log ViewerRanking in Log Management77thRanking in other categoriesNo ranking in other categoriesRanking in Log Management51stRanking in other categoriesNo ranking in other categoriesMindshare comparisonAs of March 2025, in the Log Management category, the mindshare of SolarWinds Kiwi Log Viewer is 0.0%, up from 0.0% compared to the previous year. The mindshare of SolarWinds Log Analyzer is 0.4%, down from 0.6% compared to the previous year. It is calculated based on PeerSpot user engagement data.Featured ReviewsUse our free recommendation engine to learn which Log Management solutions are best for your needs.842,194 professionals have used our research since 2012.Top IndustriesCompany SizeQuestions from the CommunityComparisonsProduct ReportsOverviewSample Customers Find out what your peers are saying about Wazuh, Splunk, Datadog and others in Log Management. Updated: March 2025.842,194 professionals have used our research since 2012.We monitor all Log Management reviews to prevent fraudulent reviews and keep review quality

2025-03-29
User9422

4 ÷ log10 2 = log10 22 ÷ log10 2= 2 log10 2 ÷ log10 2= 2 log10 2/ log10 2= 2 (1)= 2Now let us consider RHS,log3 9 = log3 32= 2 log3 3= 2(1)= 2∴ LHS = RHSHence proved.(ii) log10 25 + log10 4 = log5 25Let us consider LHS, log10 25 + log10 4log10 25 + log10 4 = log10 (25×4)= log10 100= log10 102= 2 log10 10= 2(1)= 2Now, let us consider RHS,log5 25 = log5 52= 2 log5 5= 2 (1)= 2∴ LHS = RHSHence proved.Question 5. If x = (100)a, y = (10000)b and z = (10)c, express log [(10√y)/x2z3] in terms of a, b, c.Answer:Given:x = (100)a = (102)a = 102ay = (10000)b = (104)b = 104bz = (10)cIt is given that, log [(10√y)/x2z3]log [(10√y)/x2z3] = (log 10 + log √y) – (log x2 + log z3)= (1 + log(y)1/2) – (log x2 + log z3) [we know that, log 10 = 1]= (1 + ½ log y) – (2 log x + 3 log z)Now substitute the values of x, y, z, we get= (1 + ½ log 104b) – (2 log 102a + 3 log 10c)= (1 + ½ 4b log 10) – (2×2a log 10 + 3×c log 10)= (1 + ½ 4b) – (2×2a + 3c) [Since, log 10 = 1]= (1 + 2b) – (4a + 3c)= 1 + 2b – 4a – 3cQuestion 6. If a = log10x, find the following in terms of a :(i) x(ii) log10 5√x2(iii) log10 5xAnswer:Given:a = log10x(i) x10a = x∴ x = 10a(ii) log10 5√x2log10 5√x2 = log10 (x2)1/5= log10 (x)2/5= 2/5 log10 x= 2/5 (a)= 2a/5(iii) log10 5xx = (10)a= log10 5x= log10 5(10)a= log10 5 + log10 10= log10 5 + a(1)= a + log10 5Question 7. If a =log 2/3, b = log 3/5 and c = 2 log √(5/2). Find the value of(i) a + b + c(ii) 5a+b+cAnswer:Given:a =log 2/3b = log 3/5c = 2 log √(5/2)(i) a + b + cLet us substitute the given values, we geta + b + c = log 2/3 + log 3/5 + 2 log √(5/2)= (log 2 – log 3) + (log 3 – log 5) + 2 log (5/2)1/2= log 2 – log 3 + log 3 – log 5 + 2 × ½ (log 5 – log 2)= log 2 – log 3 + log 3 – log 5 + log 5 – log 2= 0(ii) 5a+b+c5a+b+c = 50= 1Question 8. If x = log 3/5, y = log 5/4 and z = 2 log √3/2, find the value of(i) x + y – z(ii) 3x+y-zAnswer:Given:x = log 3/5 = log 3 – log 5y = log 5/4 = log 5 – log 4z = 2 log √3/2 = log (√3/2)2 = log ¾ = log 3 – log 4(i) x + y – zLet us substitute the given values, we getx + y – z = log 3 – log 5 + log 5 –

2025-04-04

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