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Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in October 2020. The graphs are generated using Desmos. This work is licensed under a Creative Commons BY 4.0 International License

Solving Exponential Equations


An exponential function is the inverse of a logarithmic function:


In an exponential function, b>0is the base of the function, y, is the exponent and, x, is the value of the exponential function.
An exponential equation is an equation which includes at least one exponential function. The simplest type of exponential equations includes exponential functions with the same basis on both sides of the equation. In this case, we use the following property: 


Example: Solve .
In order to solve this equation, we try to write both exponential functions with the same base:

Therefore, we get:


Example: Solve 
We try to write the exponentials on both sides with the same base:

We now multiply the exponents:

the above equation is equivalent to:

since the bases on both sides are equal, the exponents are equal: