## 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. under Algebra.

Solve for x in the following equation.

Example 3:

Isolate the exponential term.

Divide both sides of the equation by 8

Take the natural logarithm of both sides of the equation

The exact answers are and the approximate answers are -0.664200382745 and -6.33579961726.

Your exact answer may differ dependent how what logarithm you used to solve the problem. However, all forms of the correct answer will simplify to the same approximate answer.

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 29.

The exact answers are and the approximate answers are -0.664200382745 and -6.33579961726.

Check these answers in the original equation.

Check the solution by substituting -0.664200382745 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.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value -0.664200382745 for x, then x=-0.664200382745 is a solution.

Check the solution by substituting -6.33579961726 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.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value -6.33579961726 for x, then x=-6.33579961726 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 -6.33579961726 and -0.664200382745.. This means that -6.33579961726 and -0.664200382745 are the real solutions.

If you would like to work another example, click on Example

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 Contents.

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Author: Nancy Marcus