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 the real number x in the following equation.


Problem 7.1b:

tex2html_wrap_inline107

Answer:The exact answer is tex2html_wrap_inline109 and the approximate answer is tex2html_wrap_inline111


Solution:


The exponential term is already isolated.



Take the natural logarithm of both sides of the equation tex2html_wrap_inline113

eqnarray30



eqnarray33



eqnarray36



eqnarray39




The exact answer is tex2html_wrap_inline109 and the approximate answer is tex2html_wrap_inline117




When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 112.

eqnarray30



eqnarray46



eqnarray53



eqnarray57



eqnarray67




Check this answer in the original equation.




Check the solution tex2html_wrap_inline109 by substituting 4.499980967033 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 4.499980967033 for x, then x=4.499980967033 is a solution.




You can also check your answer by graphing tex2html_wrap_inline135 (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 4.499980967033. This means that 4.499980967033 is the real solution.


If you would like to review the answer and the solution to problem 7.1c, click on Solution.


If you would like to go back to the beginning of this section, click on Beginning.


If you would like to go to the next level of solving exponential equations, click on Next.


If you would like to go back to the equation table of contents, click on Contents.


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Author: Nancy Marcus

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