# How do you write the equation 5^-3=1/125 in logarithmic form?

Nov 14, 2016

${\log}_{5} \left(\frac{1}{125}\right) = - 3$

#### Explanation:

Using the $\textcolor{b l u e}{\text{laws of logarithms}}$

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

Consider $\frac{1}{125} = {5}^{- 3}$

$\Rightarrow x = \frac{1}{125} , b = 5 \text{ and } n = - 3$

$\Rightarrow {5}^{- 3} = \frac{1}{125} \to {\log}_{5} \left(\frac{1}{125}\right) = - 3$