We are given the logarithmic equation:

\[
\log_5(3x - 7) = 2
\]

To solve for \(x\), follow these steps:

### Step 1: Rewrite the logarithmic equation in its exponential form.
By definition, \(\log_b(a) = c\) is equivalent to \(b^c = a\). So, we can rewrite the equation:

\[
3x - 7 = 5^2
\]

### Step 2: Simplify the equation.
\[
3x - 7 = 25
\]

### Step 3: Solve for \(x\).
Add 7 to both sides:
\[
3x = 25 + 7
\]
\[
3x = 32
\]

Now, divide both sides by 3:
\[
x = \frac{32}{3}
\]

Thus, the solution is:
\[
x = \frac{32}{3}
\]

Would you like further details on this? 

Here are 5 related questions you might find helpful:
1. How do you convert a logarithmic equation to exponential form?
2. What is the inverse property of logarithms?
3. How can you solve logarithmic equations with different bases?
4. What are common mistakes to avoid when solving log equations?
5. How do you check for extraneous solutions in logarithmic equations?

**Tip:** Always check if the argument inside the logarithm is positive, since logarithms are undefined for non-positive values.

Learn how to solve the logarithmic equation ⁵log (3x-7) = 2 by converting it to exponential form. This step-by-step guide covers logarithmic and algebraic concepts, suitable for students in Grades 9-11.

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