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To solve this question, let's analyze what the expression \(\log_5 125 = 3\) means.

The expression \(\log_5 125 = 3\) states that the logarithm of 125 with base 5 is 3. This can be rewritten in exponential form as:
\[
5^3 = 125
\]

Now, let's match this with the answer choices:
- **(a) \(x^{125} = 5\)** — This does not represent the original equation \(\log_5 125 = 3\).
- **(b) \(125^3 = x\)** — This also does not match the intended relationship.
- **(c) \(x^3 = 125\)** — This does not match the original equation because it changes the base.
- **(d) \(5^3 = 125\)** — This matches our converted equation exactly.

Therefore, the correct answer is:
**(d) \(5^3 = 125\)**

Would you like more details or have any questions?

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Here are 5 related questions for further practice:
1. What is the equivalent exponential form of \(\log_2 16 = 4\)?
2. If \(\log_3 81 = 4\), what is the equivalent exponential equation?
3. How would you express \(\log_7 49 = 2\) in exponential form?
4. Which equation is equivalent to \(\log_4 64 = 3\)?
5. If \(\log_8 64 = x\), what value does \(x\) represent?

**Tip:** Remember, \(\log_b a = c\) can be converted to \(b^c = a\), which is often helpful for solving logarithmic problems in exponential terms.

Which equation is equivalent to log_5 125 = 3?

Learn how to find the equivalent exponential equation for log_5 125 = 3. This problem demonstrates converting a logarithmic expression into exponential form, applying the definition of logarithms. Suitable for students in Grades 9-11.

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