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Let's solve these logarithmic equations by converting them to their exponential forms.

### a. \( \log_2(x) = 2 \)
Convert to exponential form:
\[
2^2 = x
\]
So,
\[
x = 4
\]

### b. \( \log_4(x) = -2 \)
Convert to exponential form:
\[
4^{-2} = x
\]
Since \( 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \), we get:
\[
x = \frac{1}{16}
\]

### c. \( \log_5(x) = 4 \)
Convert to exponential form:
\[
5^4 = x
\]
Since \( 5^4 = 625 \), we get:
\[
x = 625
\]

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Would you like a more detailed explanation of the steps, or do you have any other questions? Here are five related questions that expand on this topic:

1. How do you derive the exponential form from logarithmic equations in general?
2. What is the significance of negative exponents in logarithmic expressions?
3. Can you solve for \( x \) when the base of the logarithm is a fraction (e.g., \( \log_{\frac{1}{2}}(x) = 3 \))?
4. What happens when logarithmic equations involve non-integer solutions?
5. How can logarithmic properties simplify more complex logarithmic expressions?

**Tip:** Remember, the logarithmic equation \( \log_b(x) = y \) always translates to \( b^y = x \), making it easier to solve for \( x \).

Solve for x by converting the logarithmic equation to exponential form.

Learn how to solve logarithmic equations by converting them into exponential form. This problem involves basic logarithmic and exponential concepts suitable for high school algebra students.

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