Question

Solve forx:${\log }_5\left(x\right)=-3$

Short answer

The required value ofxis$\frac{1}{125}$.

Step-by-step solution

Step 1. Given information.

Consider the given equation,

${\log }_5\left(x\right)=-3$

Compare the given equation with the standard form $x=a^y$, we get,

$$\begin{gathered} y=-3, \\ a=5, \end{gathered}$$

Step 2. Convert into exponential form.

Convert logarithmic equation into exponential equation,

$$\begin{gathered} x=a^y \\ x=5^{-3} \\ x=\frac{1}{5^3} \\ x=\frac{1}{125} \end{gathered}$$