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 7.6a:
Answer:
Exact answer: 
Approximate answer:
Solution:
The first step is to isolate 
Add 4 to both sides of the equation.
Divide both sides of the equation by 50.
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 logarithm with base 30.
Check this answer in the original equation.
Check the solution
by substituting -0.035093599722 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 -0.035093599722. This means that -0.035093599722 is the real
solution.
If you would like to review the solution to problem 7.6b, click on
Problem
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