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Question
Number of solution(s) of the equation |ln x|=|sinx| is/are
Number of solution(s) of the equation |ln x|=|sinx| is/are
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Solution
The correct option is B 2
Solution to the equation f(x)=0 is the values of x which satisfy that equation.
For the given equation, the solution will be the values of x at which |ln(x)|=|sinx|.
This means if we plot the graph of functions |sin x| and |ln x|, the points at which both the curves intersect each other are the solutions to the equation |ln(x)| = |sinx|.
Below shown is the plot of both curves on X-Y plane.
We know, ln(e) = 1
i.e., At x= e, ln(x) = 1.
For values of x > e, ln(x) > 1.
Also, sinx lies between -1 and +1.
This means that beyond x = e, |sin(x)| and |ln(x)| curve will not intersect.
We can observe that both the graphs intersect at two points.
Hence, the number of solution for the given equation is two.
Solution to the equation f(x)=0 is the values of x which satisfy that equation.
For the given equation, the solution will be the values of x at which |ln(x)|=|sinx|.
This means if we plot the graph of functions |sin x| and |ln x|, the points at which both the curves intersect each other are the solutions to the equation |ln(x)| = |sinx|.
Below shown is the plot of both curves on X-Y plane.
We know, ln(e) = 1
i.e., At x= e, ln(x) = 1.
For values of x > e, ln(x) > 1.
Also, sinx lies between -1 and +1.
This means that beyond x = e, |sin(x)| and |ln(x)| curve will not intersect.
We can observe that both the graphs intersect at two points.
Hence, the number of solution for the given equation is two.
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