e In 11 – log 33 ™ + log 100
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
simplify completely
![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
\[ 13 - m \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F068b423d-81fb-41c7-8616-9d34c4d0769a%2F0a0a5b6f-0b1f-4c52-abbb-859d4bb818a4%2Fkiu8bpd_processed.png&w=3840&q=75)
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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