Question

If $\log (x^2-21)=2$, show that $x=\pm 11$.

Answer 1

According to question,

$log(x^2-21)=2$

$\Rightarrow$ $x^2-21={10}^2$

$\Rightarrow$ $x^2=100+21$

$\Rightarrow$ $x^2=121$

$\Rightarrow$ $x{=}_{-}^{+}11$

$\Rightarrow$ $x\ne -11$ , It is the not in the domain.

Hence, $x=11$