Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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The expression in the image is: \[ e^{\ln 11} - \log_3 3^m + \log 100 \] ### Explanation: 1. **\(e^{\ln 11}\)**: - The expression \(e^{\ln x}\) simplifies to \(x\) due to the inverse properties of the exponential function and the natural logarithm. - Therefore, \(e^{\ln 11}\) simplifies to 11. 2. **\(-\log_3 3^m\)**: - This represents a logarithm with base 3. The expression simplifies due to the property \(\log_b b^x = x\). - Therefore, \(-\log_3 3^m\) simplifies to \(-m\). 3. **\(+ \log 100\)**: - This is a common logarithm (base 10). - Since \(100 = 10^2\), \(\log 100 = \log 10^2 = 2\). Using these simplifications, the entire expression becomes: \[ 11 - m + 2 \] or \[ 13 - m \]
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Transcribed Image Text:The expression in the image is: \[ e^{\ln 11} - \log_3 3^m + \log 100 \] ### Explanation: 1. **\(e^{\ln 11}\)**: - The expression \(e^{\ln x}\) simplifies to \(x\) due to the inverse properties of the exponential function and the natural logarithm. - Therefore, \(e^{\ln 11}\) simplifies to 11. 2. **\(-\log_3 3^m\)**: - This represents a logarithm with base 3. The expression simplifies due to the property \(\log_b b^x = x\). - Therefore, \(-\log_3 3^m\) simplifies to \(-m\). 3. **\(+ \log 100\)**: - This is a common logarithm (base 10). - Since \(100 = 10^2\), \(\log 100 = \log 10^2 = 2\). Using these simplifications, the entire expression becomes: \[ 11 - m + 2 \] or \[ 13 - m \]
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