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 the real number x in the following equation.

Example 4:tex2html_wrap_inline155tex2html_wrap_inline95


The exponential term is already isolated.


There is no real solution. A positive base raised to any number cannot equal a negative real number. The solution would be not be real.


Suppose you did not make this observation at first. You would have caught it in the middle of the problem.


Take the natural logarithm of both sides of the equation tex2html_wrap_inline97


eqnarray33


eqnarray37


eqnarray40



This is not a real number. The answer is that there is no real solution.


When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 26.


eqnarray33


eqnarray48


eqnarray56


eqnarray60



You can also check your answer by graphing tex2html_wrap_inline107 (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.








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


If you would like to go back to the equation table of contents, click on Contents



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Author: Nancy Marcus

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