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We are tasked with evaluating \( \log_{125} 5 \).

The logarithmic expression \( \log_{125} 5 \) asks, "What exponent do we need to raise 125 to, in order to get 5?"

Let's break this down step by step:

1. Express 125 as a power of 5:
   \[
   125 = 5^3
   \]
   This means that \( \log_{5^3} 5 = \frac{1}{3} \), because raising 125 to the power of \( \frac{1}{3} \) will give you 5.

Thus, the solution to \( \log_{125} 5 \) is \( \frac{1}{3} \).

Do you need more details or further clarifications on this? 

Here are 5 related questions for practice:
1. What is \( \log_{25} 5 \)?
2. What is \( \log_{625} 5 \)?
3. How do you simplify \( \log_{64} 4 \)?
4. What is the general formula for \( \log_{a^n} b \)?
5. How can you express \( \log_{216} 6 \)?

**Tip**: When solving logarithms, rewriting the base as a power of the argument can simplify the calculation.

Evaluate log base 125 of 5. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

Learn how to solve the logarithmic expression log base 125 of 5. This step-by-step guide shows how to express 125 as a power of 5 and use logarithmic rules to simplify the solution. Suitable for students in Grades 8-10.

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