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# Math

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 Problems Involving Exponential Equations

##### First, we have to cancel the coefficient behind the exponential function. Therefore, we divide both sides by 5: ##### We need to isolate x, to do so, we have to cancel the power of x: ##### We substitute into the original equation: ##### we multiply the exponents on the right-hand-side of the equation: ##### The base of the exponential function on the left-hand-side is 3, therefore, we try to write the right-hand-side in base 3: ##### since the bases on the right-hand-side are the same, we add their exponents: ##### the bases are equal on both sides of the equation, so, the exponents are also equal: 