How do you solve for x the exponential?e^3x*e^2x-3=2

By definition, the superscripts of two exponentials that
have matching bases and they are multiplied, must be
added.

Therefore, (e^3x)*(e^2x) = e^(3x+2x) =
e^(5x)

The equation will
become:

e^(5x) - 3 = 2

e^(5x)
= 3 + 2

e^(5x) = 5

We'll take
natural logarithms both sides:

ln e^(5x) = ln
5

We'll apply the power
rule:

5x*ln e = ln 5

But ln e
= 1

5x = ln 5

x = ln
5/5

The solution of the equation is x = (ln
5)/5.