Question

solve the following:

2^-x=3^2x+2

Answer 1

If this is your problem

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

take logarithms of both sides
-x log 2 = (2x + 2)log 3
-x log 2 = 2x log 3 + 2 log 3
-x log 2 - 2x log 3 = 2 log 3
x (-log 2 - 2 log 3) = 2 log 3
x = -(2 log 3)/(log 2 + 2 log 3)

plug in log values
x = -0.760188