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.


Problem 7.7b:

tex2html_wrap_inline227


Answer: tex2html_wrap_inline155No Real Solution


Solution:


The first step is to isolate tex2html_wrap_inline229 .


Add 20 to both sides of the equation.


tex2html_wrap_inline227


tex2html_wrap_inline235


tex2html_wrap_inline237



Divide both sides of the equation by 5.


tex2html_wrap_inline237


tex2html_wrap_inline243


tex2html_wrap_inline245



The next step is to isolate the variable x.


Take the natural logarithm of both sides of the equation..


tex2html_wrap_inline245


tex2html_wrap_inline251


tex2html_wrap_inline253


tex2html_wrap_inline255


tex2html_wrap_inline257



Use the Quadratic Formula tex2html_wrap_inline259 where a=1, b=2, tex2html_wrap_inline265


tex2html_wrap_inline267


tex2html_wrap_inline269


tex2html_wrap_inline271


tex2html_wrap_inline273


tex2html_wrap_inline275


No Real Solution


No Solution.



You can also check your answer by graphing tex2html_wrap_inline277 (formed by subtracting the right side of riginal 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 are no real solutions.








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