## 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 functions under Algebra.

Solve for x in the following equation.

Problem 7.4d:

Solution:

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.

Factor the left side of the equation

The only way that a product can equal zero is if at least one of the factors is zero.

Now let's look at the second factor,

There is no real number such that a negative number.

Check this answer in the original equation.

Check the solution by substituting -0.182321556794 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 -0.182321556794 for x, then x=-0.182321556794 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 one place: -0.182321556794. This means that -0.182321556794 is the real solution.

If you would like to review the solution to problem 7.4e, click on solution.

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Author: Nancy Marcus