To solve this problem, we can use the Change of Base Formula, which states:

$\log_b(a) = \frac{\log(a)}{\log(b)} \quad \text{or} \quad \log_b(a) = \frac{\ln(a)}{\ln(b)}$

Here, the given logarithm is $\log_3(99)$. Using the formula with either common logarithms ($\log$) or natural logarithms ($\ln$):

$\log_3(99) = \frac{\log(99)}{\log(3)} \quad \text{or} \quad \log_3(99) = \frac{\ln(99)}{\ln(3)}$

Now, let’s calculate this step by step:

Using a Calculator:

1. Compute $\log(99)$ and $\log(3)$:

   • $\log(99) \approx 1.9956$
   • $\log(3) \approx 0.4771$

2. Compute the division: $\log_3(99) = \frac{1.9956}{0.4771} \approx 4.1832$

Final Answer:

$\boxed{4.1832}$

If you want to double-check using $\ln$, the result will be the same.

Would you like a further breakdown or more details? Here are some related questions:

1. How does the change of base formula work conceptually?
2. Can this method be used with other bases, such as base $e$?
3. How would we rewrite and calculate $\log_5(625)$?
4. What are the practical applications of logarithms in real-life scenarios?
5. Can you explain the difference between $\log$ and $\ln$?

Tip: Always double-check calculator values and round intermediate results to ensure precision in the final answer!