https://file.aiquickdraw.com/mathbot/file/1727075867295zpavqz4k.jpg

The equation in the image is:

\[
5 \log 25 = 2
\]

Let's solve this step by step:

1. Start by isolating the logarithmic term:
   \[
   \log 25 = \frac{2}{5}
   \]
   
2. Convert the logarithmic equation to its exponential form:
   The logarithm \(\log 25\) is typically base 10, so we write:
   \[
   25 = 10^{\frac{2}{5}}
   \]
   
3. To simplify \(10^{\frac{2}{5}}\), we can use the property of exponents:
   \[
   10^{\frac{2}{5}} = (10^2)^{\frac{1}{5}} = 100^{\frac{1}{5}}
   \]

   The fifth root of 100 is approximately:
   \[
   100^{\frac{1}{5}} \approx 2.511
   \]

Since the left-hand side of the original equation was 25, and \(10^{\frac{2}{5}}\) approximately equals 2.511, the equation as written is not exactly true. There might be a typo in the original problem.

Would you like more details or clarifications on this?

Here are 5 related questions:
1. How do you convert logarithmic equations to exponential form?
2. What is the difference between common and natural logarithms?
3. How do you solve logarithmic equations with different bases?
4. What are the properties of logarithms that can help simplify calculations?
5. How do fractional exponents relate to roots?

**Tip:** When solving logarithmic equations, always make sure you correctly identify the base of the logarithm, which is typically 10 (common logarithm) or \(e\) (natural logarithm).

This solution explores the logarithmic equation 5 log 25 = 2, where key algebraic concepts and logarithmic properties are applied. The problem is suitable for students in Grades 10-12, covering how to isolate and simplify logarithmic expressions and their exponential counterparts.

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