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 1:
The first objective is to isolate the expression
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 100.
Take the natural logarithm of both sides of the equation
The exact answer is and the approximate answer is
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithm with base 14.
Check this answer in the original equation.
Check the solution
by substituting -0.609853334512 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.
You can also check your answer by graphing (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 -0.609853334512. This means that -0.609853334512 is the 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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