Solving Exponential Equations
Exponential equations are equations in which variables occur as exponents.
For example, exponential equations are in the form .
If is a positive number other than , then if and only if . In other words, if the bases are the same, then the exponents must be equal.
Solve the equation .
Note that the bases are not the same. But we can rewrite as a base of .
We know that, .
Rewrite as so each side has the same base.
By the property of equality of exponential functions, if the bases are the same, then the exponents must be equal.
Add to each side.
Divide each side by .