How Do You Solve An Exponential Equation?

In algebra an exponential equation has variables in the exponent of a power, rather than the base. For example, 5 = 3^x is an exponential equation because 3 is raised to the power x. These math problems are encountered in high school algebra and can be solved with logarithms.

In practical use, exponential equations occur in financial math problems involving compound interest. First, review the basic rules of logarithms. For any two positive numbers a and b, the following rules can be applied: Log(ab) = Log(a) + Log(b) Log(a/b) = Log(a) - Log(b) Log(a^b) = (b)Log(a) In the examples below, it will not matter if you use the "LOG" or "LN" buttons on your calculator.

The difference between LOG and LN is that LOG is base 10, and LN is base e=2.71828 First, practice solving a simple exponential equation. Let's use the one given in the intro 5 = 3^x. The first step is to take the logarithm of both sides, so Log(5) = Log(3^x) Using the third rule of logs, we can simplify it to Log(5) = (x)Log( ... more.

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