which expression results when the change of base formula is applied to log₄(x + 2)?\n\frac{log(x +…

which expression results when the change of base formula is applied to log₄(x + 2)?\n\frac{log(x + 2)}{log4}\n\frac{log4}{log(x + 2)}\n\frac{log4}{logx+2}\n\frac{logx + 2}{log4}

which expression results when the change of base formula is applied to log₄(x + 2)?\n\frac{log(x + 2)}{log4}\n\frac{log4}{log(x + 2)}\n\frac{log4}{logx+2}\n\frac{logx + 2}{log4}

Answer

Explanation:

Step1: Recall change - of - base formula

The change - of - base formula for logarithms is $\log_{a}b=\frac{\log_{c}b}{\log_{c}a}$, where $c$ can be any positive number other than 1. Commonly, $c = 10$ (common logarithm) or $c=e$ (natural logarithm).

Step2: Apply formula to $\log_{4}(x + 2)$

Here, $a = 4$ and $b=x + 2$. Using the change - of - base formula with base $c = 10$ (written as $\log$ for common logarithm), we get $\log_{4}(x + 2)=\frac{\log(x + 2)}{\log4}$.

Answer:

A. $\frac{\log(x + 2)}{\log4}$