When solving a problem such as 3^(2x + 1) = 9^(3x + 2), you can use logarithms or get the bases the same and set the exponents equal to each other. Getting the bases the same you have 3^(2x + 1) = 3^(6x + 4). Now set 2x + 1 = 6x + 4 and solve for x. When doing so, you get x = -3/4.

If we solve using logarithms, take the log of both sides to get

log (3^(2x+1)) = log(9^(3x + 2))

(2x + 1)log3 = (3x + 2)log9

(2x + 1)/(3x + 2) = log9/log3

(2x + 1)/(3x + 2) = 2

(2x + 1) = 2(3x + 2)

2x + 1 = 6x + 4

-4x = 3

x = -3/4