To solve the equation:

$\log_x{9} = 3$

We need to rewrite it in exponential form:

$x^3 = 9$

Now, take the cube root of both sides:

$x = \sqrt[3]{9}$

This is the simplified form of the solution. If you want a decimal approximation:

$x \approx 2.0801$

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

Here are 5 related questions for further exploration:

1. How do you solve logarithmic equations with different bases?
2. What are the properties of logarithms?
3. How do you convert logarithmic expressions to exponential form?
4. Can all logarithmic equations be solved algebraically?
5. How does changing the base of a logarithm affect the solution?

Tip: Always remember that a logarithmic equation can be rewritten in exponential form, which is often easier to solve!