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Solve for the real number x in the following equation.
Answer:The exact answer is and the approximate answer is
The exponential term is already isolated.
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 logarithmic with base 112.
Check this answer in the original equation.
Check the solution by substituting 4.499980967033 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 4.499980967033. This means that 4.499980967033 is the real solution.
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