find the exact value

Question

3^2x+1 = 5^3x

find exact value for x

thanks!

Answer 1

3^(2x+1) = 5^(3x)

(2x+1) log 3 = (3x) log 5 <--- takes log of both sides; exponents to the front

2 (log3) x + log 3 = 3 (log 5) x <--- distributive

2(log3)x - 3 (log 5)x + log 3 = 0

x [ 2 log 3 - 3 log 4] + log 3 = 0

x = (-log 3) / [ 2 log 3 - 3 log 4]