## 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.

Problem 7.4f:

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.

The left side of the equation is not easily factored. Let's see if we can use the Quadratic Formula.

Note that the equation can be rewritten as This is a quadratic equation in If it is easier for you, substitute a number, say p, in place of and rewrite the equation as let's solve this equation for p.

However, the initial equation did not contain p, therefore you have to resubstitute for p and solve for x.

There is no real number such that a negative number.

The exact answer is and the approximate answer is These answers may or may not be solutions to the original equations. You must check the answers in the original equation.

Check this answer in the original equation.

Check the solution by substituting -0.352032295516 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 -0.352032295516 for x, then x=0-0.352032295516 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: -0.352032295516. This means that -0.352032295516 is the real solution.

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

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Author: Nancy Marcus