Question

tyler applied the change of base formula to a logarithmic expression. the resulting expression is shown below.$\frac{log \frac{1}{4}}{log 12}$which expression could be tylers original expression?$circ log_{\frac{1}{4}} 12$$circ log_{12} \frac{1}{4}$$circ 12log \frac{1}{4}$$circ \frac{1}{4}log 12$

Explanation:

Step1: Recall change of base formula

The change of base formula for logarithms is $\log_b a = \frac{\log a}{\log b}$, where $\log$ represents a logarithm with any common base (e.g., base 10 or natural log).

Step2: Match result to formula

We are given $\frac{\log \frac{1}{4}}{\log 12}$. Comparing this to the change of base formula, we can identify that $a = \frac{1}{4}$ and $b = 12$. Substituting back into the left-hand side of the formula gives the original logarithm.

Answer:

$\boldsymbol{\log_{12} \frac{1}{4}}$ (the second option)