Question

If 3 to the power y = x then y = ?

Answer 1

`y=\log_3(x)`

Explanation:

`3^y=x`

`\ln(3^y)=\ln(x)`

`y\ln(3)=\ln(x)`

`y=(\displaystyle\ln(x))/(\displaystyle\ln(3))`

but if

`f(x)=(\displaystyle\ln(x))/(\displaystyle\ln(3))`

then since

`f(3)=(\displaystyle\ln(3))/(\displaystyle\ln(3))=1`

`f(x)=\log_3(x)`

so

`y=\log_3(x)`

or

`3^y=x`

`\log_3(3^y)=\log_3(x)`

`y\log_3(3)=\log_3(x)`

`\text{but }\,\log_3(3)=1, \text{so,}`

`y=\log_3(x)`