To solve the equation $\log_3 x = 4$ for $x$:

1. Recall the definition of a logarithm:
   $\log_b a = c$ means $a = b^c$, where $b$ is the base, $a$ is the argument, and $c$ is the exponent.

2. Apply the definition to $\log_3 x = 4$:
   This implies:
   $x = 3^4$

3. Simplify $3^4$:
   $3^4 = 3 \times 3 \times 3 \times 3 = 81$

Final Answer:
$x = 81$

Would you like me to explain logarithms further or go over additional examples? Let me know!

Here are some related questions you can explore:

1. What is $\log_5 125$?
2. Solve $\log_2 x = 6$.
3. How do you convert a logarithmic equation into exponential form?
4. Solve $2^{\log_2 x} = 16$.
5. What are the properties of logarithms (product, quotient, and power rules)?

Tip: Remember, logarithms are the inverse operations of exponents!