The given problem asks you to rewrite the logarithmic equation $\log_5(25) = 2$ as an exponential equation using the property from Theorem 6.2, which states that:

$b^a = c \quad \text{if and only if} \quad \log_b(c) = a$

Step-by-step solution:

You are given:

$\log_5(25) = 2$

Using the property from the theorem, $\log_b(c) = a$ can be rewritten as $b^a = c$.

In this case:

• $b = 5$,
• $a = 2$,
• $c = 25$.

So, you can rewrite the logarithmic equation $\log_5(25) = 2$ as the exponential equation:

$5^2 = 25$

This confirms that $5^2 = 25$, so the rewritten exponential form is correct.

Would you like any further clarification on this, or need help with more examples?

Related questions:

1. What is the exponential form of $\log_3(9) = 2$?
2. Can you convert $\log_{10}(1000) = 3$ into exponential form?
3. How would you rewrite $\log_7(49) = 2$ in exponential form?
4. How do you express $\log_2(8) = 3$ as an exponential equation?
5. Can you explain why $\log_b(1) = 0$ for any base $b$?

Tip:

To convert a logarithmic equation into exponential form, remember that $\log_b(c) = a$ is equivalent to $b^a = c$, which can help simplify or solve many problems related to logarithms.