How do we solve exponential equations?

Well usually we know how to solve problems like:
          x = 3^4
which will equal 81.

We know how to also solve problems when the unknown is alone:
          (3)^3 = (x^1/3)^3
which will equal; x = 3^3 = 27

We know how to solve problems where even the base is unknown:
          4 = x^2
which will equal to -2,2.

What we didn't know is this;
          100 = 10^x , but this problem is easy, x would have to equal 2 in order for this to be true.
this problem is where the unknown is actually the exponent.

          Solve for x;
2^11 = 2^x
which will equal 11.
          When the bases are the same, the exponents have to be equal as well.

Solve for x:
          2^x-3 = 4
        2^x-3 = 2^2
            x-3 = 2
            +3=+3
    _____________
Final Answer, x=5