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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 4:

The first step is to isolate the expression .

Subtract 1.4 from both sides of the equation.

Divide both sides of the equation by 2.5.

Take the natural logarithm of both sides of the equation .

Use the Quadratic Formula
where *a*=1, *b*=0, .

The exact answers are and the approximate answers are

Check these answers in the original equation.

Check the solution by substituting in the original equation for x. If the left side of the
equation equals the right side of the equation after the substitution, you
have found the correct answer.

Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value 2.34963438696 for x,
then *x*=2.34963438696 is a solution.

Check the solution by substituting in the original equation for x. If the left side of the
equation equals the right side of the equation after the substitution, you
have found the correct answer.

Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value -2.34963438696 for x,
then *x*=-2.34963438696 is a solution.

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
crosses the x-axis at . This means that 2.34963438696
and -2.34963438696 are the real solutions.

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

If you would like to go back to the equation table of contents, click on
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Author:
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