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 4: tex2html_wrap_inline157

The exponential term is already isolated.

Take the natural logarithm of both sides of the equation tex2html_wrap_inline159


eqnarray32


eqnarray42

The exact answer is and the approximate answer is tex2html_wrap_inline163

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithm with base 160.


eqnarray51


eqnarray56


eqnarray67


eqnarray78



Check this answer in the original equation.

Check the solution by substituting -4.12207451544 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 -4.12207451544 for x, then x=-4.12207451544 is a solution.



You can also check your answer by graphing tex2html_wrap_inline181 (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 -4.12207451544. This means that -4.12207451544 is the real solution.


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Author: Nancy Marcus

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