The image shows a logarithmic expression in the form:

$b^{\log_b x} = \underline{\hspace{2cm}}$

This is a fundamental property of logarithms. The expression $b^{\log_b x}$ simplifies directly to $x$. This is because the logarithm with base $b$ and the exponential function with the same base are inverse functions.

Thus, the correct answer to fill in the blank is:

$b^{\log_b x} = x$

Would you like further details or clarifications on logarithms?

Here are some additional questions you can explore:

1. How does the inverse relationship between exponentials and logarithms work?
2. What is the change of base formula in logarithms?
3. How can logarithms be used to solve exponential equations?
4. What happens when the base of a logarithm is less than 1?
5. How can logarithms be applied to real-world problems like compound interest?

Tip: Remember that understanding the properties of logarithms and exponents helps in simplifying complex equations, making it easier to solve them.