Question

Log5 (x squared - 9) = 0

Answer 1

`x=3,\:x=-3`

Explanation:

Given the equation

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

Divide both sides by
`\log _(10)\left(5\right)`

`(\log _(10)\left(5\right)\left(x^2-9\right))/(\log _(10)\left(5\right))=(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=√(f\left(a\right)),\:\:-√(f\left(a\right))`

`x=√(9),\:x=-√(9)`

as

`√(9)\:=3`

`-√(9)=-3`

Therefore,

`x=3,\:x=-3`