Question

Log5 (x squared - 9) = 0

Answer 1

Answer:

$x=3,\:x=-3$

Step-by-step explanation:

Given the equation

$\log _{10}\left(5\right)\left(x^2-9\right)=0$

Divide both sides by $\log _{10}\left(5\right)$

$\frac{\log _{10}\left(5\right)\left(x^2-9\right)}{\log _{10}\left(5\right)}=\frac{0}{\log _{10}\left(5\right)}$

Simplify

$x^2-9=0$

Add 9 to both sides

$x^2-9+9=0+9$

Simplifying

$x^2=9$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{9},\:x=-\sqrt{9}$

as

$\sqrt{9}\:=3$

$-\sqrt{9}=-3$

Therefore,

$x=3,\:x=-3$