To evaluate \(\log_4(30)\), we can use the change of base formula. The change of base formula for logarithms is:

\[
\log_b(a) = \frac{\log_c(a)}{\log_c(b)}
\]

where \(c\) is any base (commonly 10 or \(e\)).

Let's use the natural logarithm (\(\ln\)) for this calculation:

\[
\log_4(30) = \frac{\ln(30)}{\ln(4)}
\]

Now, we can approximate the values:

\[
\ln(30) \approx 3.4012
\]
\[
\ln(4) \approx 1.3863
\]

So,

\[
\log_4(30) \approx \frac{3.4012}{1.3863} \approx 2.453
\]

Thus, \(\log_4(30) \approx 2.453\).

Would you like more details on the logarithm properties or the steps involved?

Here are 5 related questions:
1. How would you apply the change of base formula to \(\log_4(100)\)?
2. What is the value of \(\log_2(30)\) using the same method?
3. How do logarithms with different bases relate to each other?
4. Can \(\log_4(30)\) be expressed in terms of \(\log_{10}\) or common logarithms?
5. What are the steps to solve \(\log_b(x) = y\) for \(x\)?

**Tip:** The change of base formula is particularly useful when you need to calculate logarithms for bases not available on standard calculators.

Learn how to evaluate \log_4(30) using the change of base formula. This step-by-step guide explains logarithmic concepts, the change of base formula, and provides an approximate solution for \log_4(30). Suitable for students in Grades 9-12.

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