The correct option is C
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.