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.