A geometry problem by Sabhrant Sachan

I found the solution by sketching the graphs of the functions. Notice that the sine function has zeros at integer values of x. So long as you know the shapes of the graphs it is not necessary to plot the graphs accurately, but you should use the facts that

$log(2.5)\lt1$ and $log(3)\gt 1$ to help work out how the log graph cuts the peaks of the sine graph.

You will find four intersection points for $x\gt 0$ and two intersection points for $x\lt 0$