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Solve for x in the following equation.
Answer:The exact answers are The approximate answers are and 1.89818568407.
There are many forms of the exact answer; however, all forms will have the same approximate answer.
Isolate the exponential term in the equation .
Divide both sides of the equation by 2
Take the natural logarithm of both sides of the equation
Solve for x using the quadratic formula where
The exact answers are and the approximate answers are and 1.89818568407.
Check these answers in the original equation.
Check the solution by substituting 1.89818568407 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.
Check the solution by substituting 0.60181431593 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 0.60181431593 and 1.89818568407. This means that 0.60181431593 and 1.89818568407 are the real solutions.
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