Question

which expression results when the change of base formula is applied to \\(\log_{4}(x + 2)\\)? \\(\frac{\log(x + 2)}{\log 4}\\) \\(\frac{\log x + 2}{\log 4}\\) \\(\frac{\log 4}{\log x + 2}\\) \\(\frac{\log 4}{\log(x + 2)}\\)

Explanation:

Step1: Recall 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 positive number not equal to 1.

Step2: Apply the Formula to $\log_4 (x + 2)$

Here, $b = 4$, $a = x + 2$, and we can use $c = 10$ (common logarithm, $\log$). So applying the formula, we get $\frac{\log (x + 2)}{\log 4}$.

Answer:

$\frac{\log(x + 2)}{\log 4}$ (the first option among the given choices)