Question

Number of solution(s) possible for the equation $\ln \left(x\right)=\sin \left(x\right)$ is/are

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

Solution to the equation $f\left(x\right)=0$ is the value of x which satisfies that equation.
For the given equation, solution is the values of x at which $\ln \left(x\right)=\sin \left(x\right)$
This means if we plot the graph of functions $\sin \left(x\right)\mathrm{and}\log \left(x\right),$
the points at which both the curve intersects each other are the solutions to the equation $\sin \left(x\right)=\log \left(x\right).$
Below shown is the plot of both curves on X-Y plane.

We know
$\ln \left(e\right)=1$
i.e., At $x=e=2.718,\ln \left(x\right)=1$
For values of $x>e,\ln \left(x\right)>1$
Also, sinx lies between -1 and +1.
This implies beyond x=e, sin(x) and ln(x) curve will not meet.
From the graph we can observe that both the curves intersect only once.
Hence, the number of solution for the given equation is one.