Respuesta :
[tex]\bf \textit{Logarithm Change of Base Rule}
\\\\
log_a b\implies \cfrac{log_c b}{log_c a}\\\\
-------------------------------\\\\
\cfrac{log\left( \frac{1}{4} \right)}{log(12)}\implies log_{12}\left( \frac{1}{4} \right)\implies log_{12}(4^{-1})\implies -log_{12}(4)[/tex]
Answer with explanation:
Options are
A. log1/4 12 B.log12 1/4 C.12log 1/4 D.1/4log12
The resulting expression of the original Logarithmic expression is given as:
[tex]\rightarrow \frac{\log{\frac{1}{4}}}{\log 12}\\\\ \text{Using the properties of log}\\\\ \frac{\log a}{\log b}=\log_{b}a\\\\\rightarrow \frac{\log{\frac{1}{4}}}{\log 12}=\log_{12}{\frac{1}{4}}}[/tex]
Option B
