Question

Find $x$, if ${\log }_5(x-7)=1$.

Answer 1

Solve the equation for $x$

Given, ${\log }_5(x-7)=1$

Using logarithm functions, we get,

$$\begin{gathered} \Rightarrow {\log }_5(x-7)=1\left[\because {\log }_{a}b=c\right] \\ \Rightarrow 5^1=x-7\left[\because a^c=b\right] \\ \Rightarrow x=5+7 \\ \Rightarrow x=12 \end{gathered}$$

Therefore, $x$ is equal to $12$.