Use properties of logarithms with the given approximations to evaluate the expression. log 5 x 0.699 and log 3x 0.477. Use one or both of these values to evaluate log , 125. log a 125 =
Use properties of logarithms with the given approximations to evaluate the expression. log 5 x 0.699 and log 3x 0.477. Use one or both of these values to evaluate log , 125. log a 125 =
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.3: Applications Of Systems Of Linear Equations
Problem 14E: Use log21=0,log22=1, and log24=2 to estimate log23.
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![**Logarithm Evaluation Exercise**
Use properties of logarithms with the given approximations to evaluate the expression.
\[
\log_a 5 \approx 0.699 \quad \text{and} \quad \log_a 3 \approx 0.477.
\]
Use one or both of these values to evaluate \(\log_a 125\).
\[
\log_a 125 = \text{[ ]}
\]
**Instructions:**
1. Recall that the number 125 can be expressed in terms of its prime factors.
2. Consider how you can utilize the logarithm values for 5 and 3 in finding \(\log_a 125\).
3. Apply properties of logarithms, such as the product, quotient, or power rules, as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70a8cbee-10b6-427b-ac1c-41a66a493bbd%2F4c261e22-1d52-48ea-be4d-f312733e429f%2F73fd54_processed.png&w=3840&q=75)
Transcribed Image Text:**Logarithm Evaluation Exercise**
Use properties of logarithms with the given approximations to evaluate the expression.
\[
\log_a 5 \approx 0.699 \quad \text{and} \quad \log_a 3 \approx 0.477.
\]
Use one or both of these values to evaluate \(\log_a 125\).
\[
\log_a 125 = \text{[ ]}
\]
**Instructions:**
1. Recall that the number 125 can be expressed in terms of its prime factors.
2. Consider how you can utilize the logarithm values for 5 and 3 in finding \(\log_a 125\).
3. Apply properties of logarithms, such as the product, quotient, or power rules, as needed.
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