Question

Solve for x in the equation below it may helpful to convert the equation into exponential form.Note x>oLog z(9)=2

Answer 1

`log_x(9)=2`

Apply log rule

`(1)/(\log _9\left(x\right))=2`

To clear the fraction multiply both sides by the L C M

`(1)/(\log _9\left(x\right))\log _9\left(x\right)=2\log _9\left(x\right)`

Simplify

`1=2\log _9\left(x\right)`
`\begin{gathered} (2\log _9\left(x\right))/(2)=(1)/(2) \\ \\ \end{gathered}`

Simplify

`\log _9\left(x\right)=(1)/(2)`

Apply log rule

`x=3`

Another method (convert the equation into the exponential form)

`\begin{gathered} \:log_x\left(9\right)=2\: \\ \\ \:x^2=9 \\ x^2=3^2 \\ \\ x=3 \end{gathered}`