https://file.aiquickdraw.com/mathbot/file/1727405970057jad05vze.jpg

The image shows two tasks that ask you to rewrite equations in different forms: logarithmic and exponential.

### Part (a): 
Rewrite \( 5^{-2} = \frac{1}{25} \) as a **logarithmic equation**.

This equation can be rewritten in logarithmic form using the general rule:
\[ a^x = b \quad \text{is equivalent to} \quad \log_a(b) = x. \]

In this case:
- The base is \( 5 \),
- The result is \( \frac{1}{25} \),
- The exponent is \( -2 \).

Thus, the logarithmic form is:
\[
\log_5\left(\frac{1}{25}\right) = -2.
\]

### Part (b):
Rewrite \( \log_2 16 = 4 \) as an **exponential equation**.

This logarithmic equation can be rewritten in exponential form using the rule:
\[ \log_a(b) = x \quad \text{is equivalent to} \quad a^x = b. \]

Here:
- The base is \( 2 \),
- The exponent is \( 4 \),
- The result is \( 16 \).

Thus, the exponential form is:
\[
2^4 = 16.
\]

Would you like any further details on logarithms or exponential equations? 

Here are 5 related questions you could explore:
1. How do you convert any logarithmic equation to exponential form?
2. Why is \( 5^{-2} = \frac{1}{25} \) true based on exponent rules?
3. Can you have a negative base in logarithmic or exponential equations?
4. What are the real-world applications of logarithmic equations?
5. How can you solve an exponential equation like \( 5^x = 25 \) without converting to logarithmic form?

**Tip:** A quick way to verify exponential equations is to calculate the power manually. For example, \( 2^4 = 2 \times 2 \times 2 \times 2 = 16 \).

Rewrite the following equations as requested:
(a) Rewrite 5^(-2) = 1/25 as a logarithmic equation.
(b) Rewrite log_2(16) = 4 as an exponential equation.

Learn how to convert between exponential and logarithmic equations. This guide covers examples such as rewriting 5^(-2) = 1/25 as a logarithmic equation and log_2(16) = 4 as an exponential equation, highlighting key algebraic concepts.

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