Step 1: Isolate the exponential part of the equation. If there are two exponential parts put one on each side of the equation.

Step 2: Take the logarithm of each side of the equation.

EXAMPLE: 5^{x-3}\ =\ 3^{2x+1}

                    \log_{ }^{ }5^{x-3}\ =\ \log_{ }^{ }3^{2x+1}

Step 3: Solve for the variable. In order to solve these equations we must know logarithms and how to use them with exponentiation.

EXAMPLE: \log_{ }^{ }5^{x-3}\ =\ \log_{ }^{ }3^{2x+1}

                  \left(x\ -3\right)\log_{ }^{ }5^{ }=\ \left(2x+1\right)\log_{ }^{ }3^{ }

                \left(x\ \log_{ }^{ }5^{ }-3\log_{ }^{ }5^{ }\right)=\ \left(2x\log_{ }^{ }3^{ }+1\log_{ }^{ }3^{ }\right)

              x\ \log_{ }^{ }5^{ }-\ 2\log_{ }^{ }3^{ }=\ 3\log_{ }^{ }5^{ }+1\log_{ }^{ }3

        x\ =\ \frac{3\log_{ }^{ }5^{ }+1\log_{ }^{ }3}{\left(\log_{ }^{ }5^{ }-\ 2\log_{ }^{ }3^{ }\right)}