## 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 the real number x in the following equation.

Problem 7.6 e:

The exact answer is

The approximate answer is

Solution:

Your first objective is to isolate the term.

Add to both sides of the equation .

Multiply both sides of the equation by 3.

Your second objective is to isolate the variable x.

Take the natural logarithm of both sides of the equation

The exact answer is and the approximate answer is

Check this answer 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.

• 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 for x, then 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 is the real solution.

If you would like to review the solution to problem 7.6f, click on Problem

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Author: Nancy Marcus