Question

Number of solution(s) of the equation $\left({\log }_{10}x\right|=\left(\mathrm{sinx}\right|$ is/are

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

Solution to the given equation is the values of x at which $\left({\log }_{10}x\right|=\left(\sin x\right|$
This means if we plot the graph of functions, $\left(\mathrm{sinx}\right|\mathrm{and}\left({\log }_{10}x\right|,$
the points at which both intersects each other are the solutions to the equation $\left({\log }_{10}x\right|=\left(\sin x\right|.$
Below shown is the plot of both curves on X-Y plane.
We know
$\mathrm{At}x=10,{\log }_{10}x=1\mathrm{For}x>10,{\log }_{10}x>1.\mathrm{Also},\left(\mathrm{sinx}\right|\mathrm{lies}\mathrm{between}0\mathrm{and}+1.\Rightarrow \left(\mathrm{sinx}\right|\mathrm{and}\left({\log }_{10}x\right|\mathrm{will}\mathrm{never}\mathrm{intersect}\mathrm{when}x>10.\mathrm{Both}\mathrm{the}\mathrm{curves}\mathrm{intersect}\mathrm{at}\mathrm{six}\mathrm{distinct}\mathrm{points}.\mathrm{Hence}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{solution}\mathrm{for}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{is}\mathrm{six}.$