Question

3^2x - 5(3^x) = -6

Answer 1

are we solving for x ?
let 3^x = y

then (3^x)^2 - 5(3^x) + 6 = 0
y^2 - 5y + 6 = 0
(y-2)(y-3) = 0
y = 2 or y = 3

then

3^x = 2
log both sides
log 3^x = log 2
x log 3 = log 2
x = log2/log3 = approx .631

or

3^x = 3
by observation, x = 1