How do you evaluate log_7(1/343)?

Oct 31, 2016

$- 3$

Explanation:

Consider the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\log}_{b} x = n \Leftrightarrow x = {b}^{n}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

here $b = 7 \text{ and } x = \frac{1}{343}$ , n is the value of the logarithm.

$\Rightarrow \frac{1}{343} = {7}^{n} \Rightarrow {7}^{-} 3 = {7}^{n} \Rightarrow n = - 3$