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.\n$\frac{log\frac{1}{4}}{log12}$\nwhich expression could be tylers original expression?\n$log_{\frac{1}{4}}12$\n$log_{12}\frac{1}{4}$\n$12log\frac{1}{4}$\n$\frac{1}{4}log12$

tyler applied the change of base formula to a logarithmic expression. the resulting expression is shown below.\n$\frac{log\frac{1}{4}}{log12}$\nwhich expression could be tylers original expression?\n$log_{\frac{1}{4}}12$\n$log_{12}\frac{1}{4}$\n$12log\frac{1}{4}$\n$\frac{1}{4}log12$

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 $c>0,c\neq1$.

Step2: Identify values in the given expression

In the expression $\frac{\log\frac{1}{4}}{\log12}$, comparing with the change - of - base formula $\frac{\log_{c}b}{\log_{c}a}$, we have $c$ as the common base of the numerator and denominator (usually 10 if no base is written), $b = \frac{1}{4}$ and $a = 12$.

Step3: Write the original logarithm

By the change - of - base formula, the original logarithm is $\log_{12}\frac{1}{4}$.

Answer:

$\log_{12}\frac{1}{4}$ (corresponding to the second option in the multiple - choice list)