The logarithmic expression $\log_3(81)$ asks for the exponent to which the base $3$ must be raised to obtain $81$.

In other words, you are solving the equation:

$3^x = 81$

We can express $81$ as a power of $3$:

$81 = 3^4$

So:

$3^x = 3^4$

Since the bases are the same, the exponents must be equal:

$x = 4$

Thus, $\log_3(81) = 4$.

Would you like more details on logarithms or have any questions?

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Here are some related questions:

1. What is the value of $\log_2(16)$?
2. How do you express $\log_5(25)$ in exponential form?
3. What is the value of $\log_{10}(1000)$?
4. Can you explain the change of base formula for logarithms?
5. How do you solve logarithmic equations?
6. What is the value of $\log_4(1/16)$?
7. How does the logarithm function behave for values less than 1?
8. What is the inverse function of a logarithm?

Tip: When solving logarithmic expressions, it's often helpful to express the argument as a power of the base to simplify the calculation.