Use properties of logarithms with the given approximations to evaluate the exp log 5x 0.699 and log 3x 0.477. Use one or both of these values to evaluat a
Use properties of logarithms with the given approximations to evaluate the exp log 5x 0.699 and log 3x 0.477. Use one or both of these values to evaluat a
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.3: Logarithmic Functions And Their Graphs
Problem 140E
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![**Topic: Evaluating Logarithmic Expressions using Approximations**
**Instructions**: Use properties of logarithms with the given approximations to evaluate the expression.
Given approximations:
- \(\log_a 5 \approx 0.699\)
- \(\log_a 3 \approx 0.477\)
**Task**: Use one or both of these values to evaluate \(\log_a 125\).
\[
\log_a 125 = \square
\]
**Notes**:
To find \(\log_a 125\), recognize that 125 can be expressed as \(5^3\). Therefore, using logarithmic properties:
\[
\log_a 125 = \log_a (5^3) = 3 \cdot \log_a 5
\]
Substitute the known value for \(\log_a 5\) into the equation to find the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70a8cbee-10b6-427b-ac1c-41a66a493bbd%2F4e0792d6-3b65-4c48-83e4-5fa5cc550a62%2Fn8jfwo_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Evaluating Logarithmic Expressions using Approximations**
**Instructions**: Use properties of logarithms with the given approximations to evaluate the expression.
Given approximations:
- \(\log_a 5 \approx 0.699\)
- \(\log_a 3 \approx 0.477\)
**Task**: Use one or both of these values to evaluate \(\log_a 125\).
\[
\log_a 125 = \square
\]
**Notes**:
To find \(\log_a 125\), recognize that 125 can be expressed as \(5^3\). Therefore, using logarithmic properties:
\[
\log_a 125 = \log_a (5^3) = 3 \cdot \log_a 5
\]
Substitute the known value for \(\log_a 5\) into the equation to find the answer.
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