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 =

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
Question
**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.
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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