https://file.aiquickdraw.com/mathbot/file/1726414092716dq46kpq9.jpg

The equation in the image is:

\[
(\alpha - 5) \log(5\alpha - 25) = 2
\]

### Steps to solve for \(\alpha\):

1. Start by simplifying the logarithmic expression inside the log function:
   \[
   5\alpha - 25 = 5(\alpha - 5)
   \]
   This simplifies the equation to:
   \[
   (\alpha - 5) \log(5(\alpha - 5)) = 2
   \]
   We can now rewrite the equation as:
   \[
   (\alpha - 5) \log(5) + (\alpha - 5) \log(\alpha - 5) = 2
   \]

2. Let’s denote \(\log(5)\) as a constant \(c\), so the equation becomes:
   \[
   (\alpha - 5) (c + \log(\alpha - 5)) = 2
   \]

3. Now, factor and solve this equation for \(\alpha\). We can approach it either by trial and error or through numerical methods.

Do you want a detailed solution on how to proceed from this point, or should I continue solving it directly?

Learn how to solve the logarithmic equation (α - 5) log(5α - 25) = 2 step by step. This problem involves key algebraic concepts, including the use of logarithmic properties. Suitable for high school students in Grades 10-12.

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