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