How do you simplify [ln(1/4)]/ln2?

Apr 23, 2016

$- 2$

Explanation:

$1$. Looking at $\ln \left(\frac{1}{4}\right)$, express $\frac{1}{4}$ in terms of $2$.

$\frac{\ln \left(\frac{1}{4}\right)}{\ln} 2$

$= \frac{\ln \left({2}^{-} 2\right)}{\ln} 2$

$2$. Use the natural logarithmic property, ${\ln}_{\textcolor{p u r p \le}{e}} \left({\textcolor{red}{m}}^{\textcolor{b l u e}{n}}\right) = \textcolor{b l u e}{n} \cdot {\ln}_{\textcolor{p u r p \le}{e}} \left(\textcolor{red}{m}\right)$, to simplify the numerator.

$\frac{- 2 \ln 2}{\ln} 2$

$3$. $\ln 2$ cancels each other out in the numerator and denominator.

$\frac{- 2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\ln 2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\ln 2}}}}$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} - 2 \textcolor{w h i t e}{\frac{a}{a}} |}}}$