Use common logarithms or natural logarithms and a calculator to evaluate the following.

log Subscript 12 Baseline 88.5log1288.5

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Part 1

Evaluate the expression.

log Subscript 12 Baseline 88.5log1288.5almost equals≈enter your response here

​(Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as​ needed.)

To evaluate \( \log_{12}(88.5) \), you can use the change of base formula:

\[
\log_{12}(88.5) = \frac{\log_{10}(88.5)}{\log_{10}(12)}
\]

Let's calculate this using a calculator:

1. Compute \( \log_{10}(88.5) \).
2. Compute \( \log_{10}(12) \).
3. Divide the result from step 1 by the result from step 2.

I'll calculate this now.The value of \( \log_{12}(88.5) \) is approximately \( 1.8041 \) when rounded to four decimal places.

Would you like more details on this process or have any questions?

Here are some related questions:

1. How do you apply the change of base formula to evaluate logarithms?
2. What is the importance of logarithms in solving exponential equations?
3. Can logarithms be negative or zero? If so, under what conditions?
4. How do you solve logarithmic equations with variables in the base?
5. What are the common mistakes to avoid when calculating logarithms?
6. How can you evaluate logarithms without a calculator?
7. What is the inverse function of a logarithm?
8. How do natural logarithms differ from common logarithms in practical applications?

**Tip:** Double-check your logarithmic calculations by converting them back to exponential form to see if the results make sense.

Learn how to evaluate the logarithm \( \log_{12}(88.5) \) using the change of base formula in logarithms. Step-by-step solution provided with calculations. Suitable for advanced high school students.

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