## 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 7.6b:

Solution:

The first step is to isolate

Add 10 to both sides of the equation.

Divide both sides of the equation by 6.

The next is to isolate the variable x.

Take the natural logarithm of both sides of the equation

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithm with base 12.

Check this answer in the original equation.

Check the solution by substituting 6.72105705435 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 6.72105705435 for x, then x=6.72105705435 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 6.72105705435. This means that 6.72105705435 is the real solution.

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

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Author: Nancy Marcus