Question

Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below. logc1/4 / log12 Which expression could be Tyler’s original expression?

Answer 1

`\bf \textit{Logarithm Change of Base Rule} \\\\ log_a b\implies \cfrac{log_c b}{log_c a}\\\\ -------------------------------\\\\ \cfrac{log\left( (1)/(4) \right)}{log(12)}\implies log_(12)\left( (1)/(4) \right)\implies log_(12)(4^(-1))\implies -log_(12)(4)`

Answer 2

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:

`\rightarrow \frac{\log{(1)/(4)}}{\log 12}\\\\ \text{Using the properties of log}\\\\ (\log a)/(\log b)=\log_(b)a\\\\\rightarrow \frac{\log{(1)/(4)}}{\log 12}=\log_(12){(1)/(4)}}`

Option B