The number of solution(s) of the equation `sinx = log_(10) x` is/are

Answer

Three solutions

Explanation

We have `sin x = log_(e)x`
To find the number of roots of above equation, we draw the graphs of `y = sin x` and `y =log_(10) x` and count the number of points of intersection.
Now, `sin x in [-1, 1]`.
Further, we know that `y=log_(10)x` always increases.
So, `y=log_(10)x` will never intersect `y= sin x`, when `log__(10) x gt 1` or `x gt 10`.
Graphs of both functions are as shown in the following figure.

From the figure, we can see that graphs intersect at three points.