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SOLVING EXPONENTIAL EQUATIONS

Note:

- To solve an exponential equation, isolate the exponential term, take
the logarithm of both sides and solve.

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:

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

Let's rewrite the equation with the following
substitutions: and

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 (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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Author:
Nancy Marcus

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