tyler applied the change of base formula to a logarithmic expression. the resulting expression is shown…

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?$log_{\frac{1}{4}} 12$$log_{12} \frac{1}{4}$$12log \frac{1}{4}$$\frac{1}{4}log 12$

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?$log_{\frac{1}{4}} 12$$log_{12} \frac{1}{4}$$12log \frac{1}{4}$$\frac{1}{4}log 12$

Answer

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 (like base 10 or natural base $e$).

Step2: Match given expression to formula

We are given $\frac{\log \frac{1}{4}}{\log 12}$. Comparing this to the formula $\frac{\log a}{\log b}$, we identify $a = \frac{1}{4}$ and $b = 12$. Substituting back into the original logarithmic form gives $\log_{12} \frac{1}{4}$.

Step3: Verify against options

Check that this matches one of the provided multiple-choice options.

Answer:

B. $\log_{12} \frac{1}{4}$