Question

Solve for x:

$\log \left(x^2-39\right)=1$

Short answer

The value of$x$is$\pm 7$

Step-by-step solution

Step 1. Given

An expression is given as$\log \left(x^2-39\right)=1$

Step 2. Calculation

First convert it into exponential form,

$\log \left(x^2-39\right)=1\to x^2-39={10}^1$

Now simplify it,

$$\begin{gathered} x^2-39=10 \\ {x}^2=49 \\ x=\pm \sqrt{49} \\ x=\pm 7 \end{gathered}$$

Step 3. Verification

Put the values in the original equation,

$\begin{array}{r}\log \left(7^2-39\right)=1\\ \log (49-39)=1\\ \log 10=1\\ 1=1\end{array}$

and

$\begin{array}{r}\log \left[(-7{)}^2-39\right]=1\\ \log (49-39)=1\\ \log 10=1\\ 1=1\end{array}$

In both cases LHS is equal to RHS.