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 1:tex2html_wrap_inline155tex2html_wrap_inline134


The first objective is to isolate the expression tex2html_wrap_inline136


Subtract 6 from both sides of the equation.


eqnarray29



Divide both sides of the equation by 100.


eqnarray35



Take the natural logarithm of both sides of the equation tex2html_wrap_inline142


eqnarray51


eqnarray56


eqnarray58



The exact answer is tex2html_wrap_inline144 and the approximate answer is tex2html_wrap_inline146


When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithm with base 14.


eqnarray65


eqnarray70


eqnarray80


eqnarray86



Check this answer in the original equation.



Check the solution tex2html_wrap_inline144 by substituting -0.609853334512 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 -0.609853334512 for x, then x= -0.609853334512 is a solution.


You can also check your answer by graphing tex2html_wrap_inline164 (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 -0.609853334512. This means that -0.609853334512 is the real solution.








If you would like to work another example, click on Example


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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