Question

Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.)
4x − 3 = 32x
x = _____

Answer 1

I assume you meant

4^(x-3) = 32^x
Since 4=2^2 and 32=2^5, we have
2^(2x-6) = 2^(5x)
2x-6 = 5x
3x = -6
x = -2

Check: 4^(-5) = 2^-10
32^(-2) = 2^-10

Answer 2

no it looks more like this:

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