To simplify the expression $7^{\log_7 x}$, we can use a fundamental property of logarithms and exponents.

Property:

If $a^{\log_a b} = b$, where $a$ and $b$ are positive numbers, then the expression simplifies directly to $b$.

Applying this to your problem:

Given: $7^{\log_7 x}$

By the property mentioned above: $7^{\log_7 x} = x$

Thus, $7^{\log_7 x}$ simplifies to $x$.

Final answer:

$7^{\log_7 x} = x$

Would you like more details or examples about logarithms and exponents?

Here are 5 related questions to help expand on this concept:

1. What is the inverse relationship between exponents and logarithms?
2. How can we solve for $x$ when given an equation like $3^{\log_3 x} = 81$?
3. How does the property $a^{\log_a x} = x$ apply to other bases like 10 or $e$?
4. What would happen if we had $7^{\log_7 (2x)}$?
5. Can this property be applied in cases where the base and the logarithm are different?

Tip: Understanding the relationship between exponents and logarithms can make simplifying complex expressions much easier.