The question asks you to solve the equation:

$\log_x(27) = 3$

Step-by-Step Solution:

1. Definition of Logarithms: The logarithmic equation $\log_x(27) = 3$ means: $x^3 = 27$

2. Solve for $x$: To find $x$, take the cube root of both sides: $x = \sqrt[3]{27}$

3. Evaluate the Cube Root: The cube root of 27 is: $x = 3$

Final Answer:

$x = 3$

If you have more questions or want further details, feel free to ask!

Here are 5 related questions to explore logarithms and exponents further:

1. What is the solution to $\log_x(81) = 4$?
2. If $\log_2(x) = 5$, what is $x$?
3. How can you rewrite $\log_x(y) = z$ in exponential form?
4. What are the properties of logarithms (e.g., product, quotient, power rule)?
5. What is $\log_3(9)$ and how do you calculate it?

Tip: To solve logarithmic equations efficiently, always rewrite them in their exponential form!