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 3:tex2html_wrap_inline155tex2html_wrap_inline170


Isolate the exponential term.


eqnarray29


eqnarray41



Take the natural logarithm of both sides of the equation tex2html_wrap_inline172


eqnarray50



The exact answer is tex2html_wrap_inline174 and the approximate answer is tex2html_wrap_inline176



When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 6.


eqnarray41


eqnarray72


eqnarray83


eqnarray89


eqnarray96


eqnarray111



Check this answer in the original equation.



Check the solution tex2html_wrap_inline182 by substituting -0.980829253012 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 -0.980829253012 for x, then x=-0.980829253012 is a solution.


You can also check your answer by graphing tex2html_wrap_inline194 (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 -0.980829253012. This means that -0.980829253012 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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