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Let's solve the equation step by step.

The equation given is:

\[
\frac{13^5}{13^x} = 13^4
\]

To solve for \( x \), we can use the property of exponents:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Applying this to the left side of the equation:

\[
\frac{13^5}{13^x} = 13^{5-x}
\]

Now the equation becomes:

\[
13^{5-x} = 13^4
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
5 - x = 4
\]

Now, solve for \( x \):

\[
5 - 4 = x
\]

\[
x = 1
\]

So, the solution is \( \boxed{1} \).

Would you like a detailed explanation or have any other questions?

Here are five related questions you might consider:
1. How do you solve exponential equations when the bases are different?
2. What are some other properties of exponents that are useful in solving equations?
3. How can you solve exponential equations when the exponents are variables?
4. What is the general strategy for solving equations involving fractions with exponents?
5. Can you apply logarithms to solve exponential equations? How?

**Tip:** When solving exponential equations, always try to express both sides of the equation with the same base, which allows you to equate the exponents directly.

Learn how to solve the exponential equation 13^(5-x) = 13^4 step-by-step. This problem involves exponents and equations, utilizing the exponentiation rule. Suitable for high school students in Grades 9-12.

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