SOLVING EXPONENTIAL EQUATIONS
SOLVING EXPONENTIAL EQUATIONS 
Note:
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 7.3a:
Answer:
The exact answer is 
or 
The approximate answer is 
.
Solution:
Isolate the exponential term.
Divide both sides of the equation by 5
Take the natural logarithm of both sides of the equation 
The exact answer is 
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
0.514809708591 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.
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 0.514809708591. This
means that 0.514809708591 is the real solution.
If you would to review the answer and solution to problem 7.3b, click
on Solution.
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