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.

Problem 7.6d: tex2html_wrap_inline155tex2html_wrap_inline199

Answer:

Exact answer: tex2html_wrap_inline155 tex2html_wrap_inline201 Approximate answer: tex2html_wrap_inline155 tex2html_wrap_inline203


Solution:

The first step is to isolate tex2html_wrap_inline205


Subtract .921 from both sides of the equation.


eqnarray42



Divide both sides of the equation by .278.


eqnarray54



The next step is to isolate the variable x.


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


eqnarray72


eqnarray79


eqnarray90


eqnarray100


eqnarray116


eqnarray124



The exact answer is tex2html_wrap_inline213 and the approximate answer is tex2html_wrap_inline215



Check the solution tex2html_wrap_inline213 by substituting tex2html_wrap_inline219 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 -1.065824 for x, then x=-1.065824 is a solution.


You can also check your answer by graphing the function tex2html_wrap_inline229 (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 -1.065824. This means that -1.065824 is the real solution.








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