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.
Problem 7.5d:
Answer: The exact solution is and the approximate solution
is 
Solution:
The exponential term is already isolated.
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 6.
Check this answer in the original equation.
Check the solution by substituting -2.98759384204 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 -2.98759384204. This means that -2.98759384204 is the real
solution.
If you would like to go back to the equation table of contents, click on contents.
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