If you would like an in-depth review of logarithms, the rules of logarithms, logarithmic functions and logarithmic equations, click on logarithmic functions.
Solve for x in the following equation.
Answers: There are an infinite number of solutions: are the exact solutions, and are the approximate solutions.
To solve for x, first isolate the tangent term.
If we restrict the domain of the cosine function to
we can use the arctan function to solve for x.
Since the period is this means that the values will repeat every radians. Therefore, the solutions are where n is an integer.
These solutions may or may not be the answers to the original problem. You much check them, either numerically or graphically, with the original equation.
Check the answer x=5.25825
Since the left side equals the right side when you substitute 5.25825 for x, then 5.25825 is a solution.
Check the answer
Since the left side equals the right side when you substitute 20.966214for x, then 20.966214 is a solution.
Graph the equation
Note that the graph crosses the x-axis many times indicating many solutions.
Note the graph crosses at 5.25825 (one of the solutions). Since the period of the function is , the graph crosses again at 5.25825+15.70796=2.966214 and again at , etc.
If you would like to review the solution to problem 9.2d, click on solution.
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