Question

Express 3^2 = x as a logarithmic equation.

Answer 1

`\hbox{if } a^b=c \hbox{ then} \log_a c=b \\ \\ 3^2=x \\ \Downarrow \\ \log_3 x=2`

Answer 2

`\log_3x=2`

Explanation:

The given equation is

`3^2=x`

We need to express this equation as a logarithmic equation.

Taking log base 3 on both sides.

`\log_33^2=\log_3x`

Using the property of logarithm, we get

`2=\log_3x`
`[\because \log_aa^b=b]`

Interchange the sides.

`\log_3x=2`

Hence, the required equation is
`\log_3x=2`.