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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 the real number x in the following equation.**

Problem 7.6 e:

Answer:

The exact answer is
The approximate answer is

Solution:
Your first objective is to isolate the term.

Add to both sides of the equation .

Multiply both sides of the equation by 3.

Your second objective 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 this answer in the original equation.

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.

Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value
for x, then 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 This means that is the real
solution.

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

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Author:
Nancy Marcus

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