Question

3²x+³(3x-²)=81 solve exponential equation

Answer 1

Since you mention "exponential", I suspect the equation is supposed to read

$3^{2x+3} 3^{x-2} = 81$

Recall that $a^ba^c = a^{b+c}$, so we can simplify the left side to get

$3^{(2x+3)+(x-2)} = 81$

and since 81 = 3⁴,

$3^{(2x+3)+(x-2)} = 3^4 \implies (2x+3) + (x - 2) = 4$

because the bases in the expressions on either side are the same.

Solve for x :

(2x + 3) + (x - 2) = 4

3x + 1 = 4

3x = 3

x = 1