To calculate \( \log_3(59000) \), we can apply the change of base formula, which states:

\[
\log_b(x) = \frac{\log(x)}{\log(b)}
\]

Here, \( b = 3 \) and \( x = 59000 \). So,

\[
\log_3(59000) = \frac{\log(59000)}{\log(3)}
\]

Let me calculate this for you.The value of \( \log_3(59000) \) is approximately \( 9.999 \).

Would you like further details on the calculation or related concepts?

Here are 5 related questions to explore:
1. What is the change of base formula and when is it used?
2. How would you calculate \( \log_3(100000) \)?
3. Can logarithmic identities simplify expressions like \( \log_3(59000) \)?
4. How do natural logs relate to common logarithms?
5. What are some applications of logarithms in real-world problems?

**Tip:** When using logarithms in different bases, remember that the change of base formula simplifies complex calculations into easier-to-handle base-10 or natural logarithms.

Learn how to solve log3(59000) using the change of base formula. This logarithmic problem is solved step-by-step, applying the formula log_b(x) = log(x) / log(b). Suitable for students in Grades 10-12, this problem explores key logarithmic concepts.

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