## 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 7.3c:

There are many forms of the exact answer; however, all forms will have the same approximate answer.

Solution:

Isolate the exponential term in the equation .

Divide both sides of the equation by 2

Take the natural logarithm of both sides of the equation

Solve for x using the quadratic formula where

Check these answers in the original equation.

Check the solution by substituting 1.89818568407 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 1.89818568407 for x, then x=1.89818568407 is a solution.

Check the solution by substituting 0.60181431593 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 0.60181431593 for x, then x=0.60181431593 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 0.60181431593 and 1.89818568407. This means that 0.60181431593 and 1.89818568407 are the real solutions.

If you would to review the answer and solution to problem 7.3d, click on Solution.

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If you would like to go to the next level, click on Next.

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Author: Nancy Marcus