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. under Algebra.

Solve for x in the following equation.

Example 1: tex2html_wrap_inline155tex2html_wrap_inline131

Isolate the exponential term.

eqnarray26



Take the natural logarithm of both sides of the equation tex2html_wrap_inline133


eqnarray34


eqnarray37


eqnarray41


eqnarray44



The exact answer is tex2html_wrap_inline135 and the approximate answer is tex2html_wrap_inline137


When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 5.


eqnarray34


eqnarray52


eqnarray60


eqnarray65


eqnarray72


eqnarray79


eqnarray86



Check this answer in the original equation.



Check the solution tex2html_wrap_inline143 by substituting 4.00733318523 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 4.00733318523 for x, then x=4.00733318523 is a solution.


You can also check your answer by graphing tex2html_wrap_inline155 (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 4.00733318523. This means that 4.00733318523 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 onProblem.


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