Question

Solve the exponential equation 9^2x = 27

Answer 1

27 = 9^(3/2) 
.
so x = 4/3

Answer 2

Answer:

The value of x is,  $\frac{3}{4}$

Explanation:

Given:

The exponential equation $9^{2x} =27$        ....[1]

Exponential Identities:

$(x^a) =x^{ab}$

we can write equation [1] as;

$(3^2)^{2x} = 3^3$     [ $3 \times 3= 9 , 3 \times 3 \times 3 = 27$ 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:

$x = \frac{3}{4}$