If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function.

Solve for x in the following equation.

Example 5: tex2html_wrap_inline155 tex2html_wrap_inline98

In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.

We cannot easily factor this problem. Therefore, let's see if we can use the Quadratic Formula to solve the problem even thought the equation does not look like a quadratic equation. In fact, it is a quadratic equation in tex2html_wrap_inline100

Let's rewrite the equation tex2html_wrap_inline102 with the following substitutions: tex2html_wrap_inline104 and tex2html_wrap_inline106


Now you should recognize this as a quadratic equation in t where a=2, b=5, and c=6.



No real solutions.

You can also check your answer by graphing tex2html_wrap_inline116 (formed by subtracting the right side of the original equation from the left side). Look to see where the graph crosses the x-axis; that will be the real solution. Note that the graph never crosses the x-axis. This means that there are no real solutions

If you would like to test yourself by working some problems similar to this example, click on Problem

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