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.

Problem 7.6d:

Solution:

The first step is to isolate

Subtract .921 from both sides of the equation.

Divide both sides of the equation by .278.

The next step 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 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 -1.065824 for x, then x=-1.065824 is a solution.

You can also check your answer by graphing the function (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 -1.065824. This means that -1.065824 is the real solution.

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

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Author: Nancy Marcus