## 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.

Example 1:

Isolate the exponential term.

Divide both sides of the equation by 4

Take the natural logarithm of both sides of the equation

The exact answer is ( which can also be written ) and the approximate answer is

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 5.

Check this answer in the original equation.

Check the solution

(can also be written in the equivalent form )

by substituting 0.111571775657 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 0.111571775657 for x, then x=0.111571775657 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 0.111571775657. This means that 0.111571775657 is the real solution.

If you would like to work another example, click on Example

If you would like to test yourself by working some problems similar to this example, click on Problem

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Author: Nancy Marcus