Answer:
[tex]x=3,\:x=-3[/tex]
Step-by-step explanation:
Given the equation
[tex]\log _{10}\left(5\right)\left(x^2-9\right)=0[/tex]
Divide both sides by [tex]\log _{10}\left(5\right)[/tex]
[tex]\frac{\log _{10}\left(5\right)\left(x^2-9\right)}{\log _{10}\left(5\right)}=\frac{0}{\log _{10}\left(5\right)}[/tex]
Simplify
[tex]x^2-9=0[/tex]
Add 9 to both sides
[tex]x^2-9+9=0+9[/tex]
Simplifying
[tex]x^2=9[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]x=\sqrt{9},\:x=-\sqrt{9}[/tex]
as
[tex]\sqrt{9}\:=3[/tex]
[tex]-\sqrt{9}=-3[/tex]
Therefore,
[tex]x=3,\:x=-3[/tex]
