To compute $\log_3(120)$, we can use the change of base formula for logarithms:

$\log_b(x) = \frac{\log(x)}{\log(b)}$

Where $\log$ is the common logarithm (base 10) or natural logarithm (base $e$).

Using this formula, we can rewrite $\log_3(120)$ as:

$\log_3(120) = \frac{\log(120)}{\log(3)}$

Now, calculating each value:

• $\log(120) \approx 2.07918$
• $\log(3) \approx 0.47712$

Thus:

$\log_3(120) = \frac{2.07918}{0.47712} \approx 4.36$

So, $\log_3(120) \approx 4.36$.

Would you like further explanation or details on logarithms? Here are some related questions to explore:

1. What is the difference between common logarithms and natural logarithms?
2. How do you use logarithms to solve exponential equations?
3. What is the relationship between logarithms and exponents?
4. Can you simplify $\log_3(27)$ directly without a calculator?
5. How do logarithms help in solving real-world problems?

Tip: Logarithms are particularly useful for dealing with large numbers or exponential growth, such as in compound interest or population models.