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 7.1d:

tex2html_wrap_inline51


Answer:There is no real answer.


Solution:


If you did not make this observation early on, you'd catch it during the process of solving or checking your answer.


Take the natural logarithm of both sides of the equation tex2html_wrap_inline53

eqnarray30



You cannot take the natural logarithm of a negative number and come up with a real number answer.




You can also check your answer by graphing tex2html_wrap_inline55 (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 never crosses the x-axis. This means that there is no real solution.


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


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Author: Nancy Marcus

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