To calculate the value of $\log_3(15)$, we can use the change of base formula, which is:

$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$

For simplicity, we typically use base 10 (common logarithms) or base $e$ (natural logarithms). Using base 10, the expression becomes:

$\log_3(15) = \frac{\log(15)}{\log(3)}$

Now, let's calculate:

$\log(15) \approx 1.1761$ $\log(3) \approx 0.4771$

Therefore:

$\log_3(15) \approx \frac{1.1761}{0.4771} \approx 2.465$

So, $\log_3(15) \approx 2.465$.

Would you like further details on logarithms, or do you have any questions?

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Here are 5 related questions to explore:

1. How do you solve logarithmic equations involving different bases?
2. What are the properties of logarithms and how are they applied?
3. How can logarithms help in solving exponential growth or decay problems?
4. What is the natural logarithm, and when is it used instead of common logarithms?
5. How can you convert between logarithms of different bases?

Tip: Logarithmic identities like the change of base formula can simplify solving problems with unfamiliar bases!