https://file.aiquickdraw.com/mathbot/file/1729575163458thnsyvq2.jpg

Let's solve the given equation:

The problem is:  
\[
5^{4x} = 125
\]

### Step 1: Express both sides using the same base
Since \(125 = 5^3\), we can rewrite the equation as:
\[
5^{4x} = 5^3
\]

### Step 2: Use the property of exponents
When the bases are the same, we equate the exponents:
\[
4x = 3
\]

### Step 3: Solve for \(x\)
\[
x = \frac{3}{4}
\]

### Final Answer:
The solution is:
\[
x = \frac{3}{4}
\]

So the correct choice is:  
**A. The solution is \(x = \frac{3}{4}\)**

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Do you have any follow-up questions or want further details?

Here are five related questions to explore further:
1. How do you solve an equation where the bases are not easily matched?
2. What are the properties of exponents that help solve such equations?
3. What if the equation was \(5^{4x} = 1\)? How would the solution change?
4. How can logarithms be used to solve similar problems?
5. What if the original equation involved negative exponents? How would the steps change?

**Tip:** In equations involving powers, if the bases are identical, equating the exponents is a quick way to find the solution.

Solve for x in the equation 5^(4x) = 125.

Learn how to solve the exponential equation 5^(4x) = 125 with a step-by-step solution. The solution involves using exponent properties to simplify and solve for x. Suitable for students in Grades 8-10.

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