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.

Example 4:tex2html_wrap_inline155tex2html_wrap_inline294


Your first objective is to isolate the expression. tex2html_wrap_inline296


Add tex2html_wrap_inline298 to both sides of the equation tex2html_wrap_inline294 .


eqnarray49


eqnarray64


eqnarray88



Multiply both sides of the equation tex2html_wrap_inline302 by tex2html_wrap_inline304


eqnarray116


eqnarray140



Your second objective is to isolate the variable x.


Take the natural logarithm of both sides of the equation tex2html_wrap_inline306


eqnarray159


eqnarray166


eqnarray177


eqnarray191


eqnarray207




The exact answer is tex2html_wrap_inline308 and the approximate answer is tex2html_wrap_inline310



Check this answer in the original equation.



Check the solution tex2html_wrap_inline308 by substituting -0.501676693208 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 -0.501676693208 for x, then x=-0.501676693208 is a solution.


You can also check your answer by graphing tex2html_wrap_inline328 (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 -0.501676693208. This means that -0.501676693208 is the real solution.








If you had trouble with the fractions and would like a review of fractions, click on Fractions


If you would like to test yourself by working some problems similar to this example, click on Problem


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Author: Nancy Marcus

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