Answered

Solve the exponential equation

9^2x = 27

Verified Answer :

27 = 9^(3/2) 
.
so x = 4/3

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:

\(x = \frac{3}{4}\)

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