Question

Solve the exponential equation
9^2x = 27

Answer 1

27 = 9^(3/2)
.
so x = 4/3

Answer 2

The value of x is,
`(3)/(4)`

Step-by-step explanation:

Given:

The exponential equation
`9^(2x) =27` ....[1]

Exponential Identities:

`(x^a) =x^(ab)`

we can write equation [1] as;

`(3^2)^(2x) = 3^3` [
`3 * 3= 9 , 3 * 3 * 3 = 27` we can rewrite as
`3^2 =9 , 3^3 =27`]

by using above identities, we have

`(3)^(4x) = 3^3` then,

`4x =3` [ if
`x^a =x^b` then a =b]

Simplify:

`x = (3)/(4)`