https://file.aiquickdraw.com/mathbot/file/172718665725607ny5xy2.jpg

Let's solve each of the given problems step by step:

### (a) \( \log(0.0270) \)
This is a logarithm with base 10 (common logarithm).

\[
\log(0.0270) \approx -1.5686
\]

### (b) \( \ln(47.89) \)
This is the natural logarithm (logarithm with base \(e\)).

\[
\ln(47.89) \approx 3.868
\]

### (c) \( \log_7(126.4) \)
For this, we will use the change of base formula:
\[
\log_b(a) = \frac{\log(a)}{\log(b)}
\]
Here, \(a = 126.4\) and \(b = 7\).

\[
\log_7(126.4) = \frac{\log(126.4)}{\log(7)} \approx \frac{2.1014}{0.8451} \approx 2.487
\]

### Final Results:
- (a) \( \log(0.0270) \approx -1.5686 \)
- (b) \( \ln(47.89) \approx 3.868 \)
- (c) \( \log_7(126.4) \approx 2.487 \)

Would you like a detailed explanation of any of the steps?

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Here are 5 related questions to explore further:
1. What is the change of base formula, and why is it used?
2. How does the logarithm of a number less than 1 result in a negative value?
3. What are the differences between common logarithms and natural logarithms?
4. How can logarithms be used to solve exponential equations?
5. What are some real-world applications of logarithmic calculations?

**Tip:** Always remember to check the base of the logarithm when solving problems, as it determines the method you use for calculations.

Evaluate by calculator or by change of base where necessary: (a) log 0.0270, (b) ln 47.89, (c) log_7 126.4

Learn how to solve logarithmic problems such as log 0.0270, ln 47.89, and log base 7 of 126.4 using a calculator and change of base formula. This problem covers logarithmic concepts and change of base theorem, suitable for high school students in Grades 10-12.

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