Yes, the equation $\log_a(a^x) = x$ is correct.

This is a fundamental property of logarithms known as the logarithm-exponential identity. Here's why it holds true:

Explanation:

1. The logarithm $\log_a(y)$ is defined as the power to which the base $a$ must be raised to obtain the number $y$. In other words, $\log_a(y) = x$ implies that $a^x = y$.

2. Given the expression $\log_a(a^x)$, you're essentially asking, "To what power must $a$ be raised to get $a^x$?"

3. Since $a$ raised to the power $x$ is simply $a^x$, the answer is $x$. Therefore: $\log_a(a^x) = x$

This property is true for any positive base $a$ (where $a \neq 1$) and any real number $x$.

Would you like to explore more about logarithms or see examples?

Related Questions:

1. What are other fundamental properties of logarithms?
2. How does the change of base formula for logarithms work?
3. What is the inverse relationship between logarithms and exponentiation?
4. How can logarithms be used to solve exponential equations?
5. What is the significance of the natural logarithm $\ln(x)$?

Tip: Understanding the properties of logarithms can greatly simplify solving complex logarithmic and exponential equations.