Solve for x, given that : e^(3x)=12.

We notice that the unknown is in superscript. To determine
the variable, we'll have to take natural logarithms both sides (we'll take natural
logarithms instead of decimal logarithms because the exponential functionhas the base =
e).

ln [e^(3x)] = ln 12

We'll
apply power rule of logarithms:

3x ln e = ln
12

But ln e = 1 and the equation will
become:

3x = ln 12

We'll
divide by 3:

x = (1/3)*ln
12

We'll apply again the power
rule:

x = ln
12^(1/3)

The solution of the equation is:

x = ln
12^(1/3).