ving logarithmic equations using technology\ntyler applied the change of base formula to a logarithmic…

ving logarithmic equations using technology\ntyler applied the change of base formula to a logarithmic expression. the resulting expression is shown.\n$\frac{log \frac{1}{4}}{log 12}$\nwhich expression could be tylers original expression?\n$log_{12} \frac{1}{4}$\n$12log \frac{1}{4}$\n$log_{\frac{1}{4}} 12$\n$\frac{1}{4}log 12$

ving logarithmic equations using technology\ntyler applied the change of base formula to a logarithmic expression. the resulting expression is shown.\n$\frac{log \frac{1}{4}}{log 12}$\nwhich expression could be tylers original expression?\n$log_{12} \frac{1}{4}$\n$12log \frac{1}{4}$\n$log_{\frac{1}{4}} 12$\n$\frac{1}{4}log 12$

Answer

Explanation:

Step1: Recall change of base formula

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

Step2: Match result to original expression

The given result is $\frac{\log \frac{1}{4}}{\log 12}$. Comparing this to the change of base formula, we identify $b=12$ and $a=\frac{1}{4}$. Substituting back into the left side of the formula gives the original expression.

Answer:

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