Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is D 5

Solution to the equation $f\left(x\right)=0$ is the value of x which satisfies that equation.
For the given function, we have to find the number of values of x at which ${\log }_{10}x=\left|\mathrm{sinx}\right|.$
This means if we plot the graph of functions $\left|\sin x\right|\mathrm{and}{\log }_{10}x,$the points at which both intersects each other are the solutions to the equation ${\log }_{10}x=\left|\sin x\right|.$
Below shown is the plot of both curves on X-Y plane.
$\mathrm{We}\mathrm{know}\mathrm{At}x=10,{\log }_{10}x=1\mathrm{For}\mathrm{values}\mathrm{of}x>10,{\log }_{10}x>1.\mathrm{Also},\left(\mathrm{sinx}\right|\mathrm{lies}\mathrm{between}0\mathrm{and}+1.\mathrm{So},\mathrm{these}\mathrm{curves}\mathrm{will}\mathrm{never}\mathrm{intersect}\mathrm{for}x>10.\mathrm{From}\mathrm{the}\mathrm{graph},\mathrm{we}\mathrm{can}\mathrm{observe}\mathrm{that}\mathrm{these}\mathrm{curves}\mathrm{intersect}\mathrm{at}5\mathrm{points}.\mathrm{Hence}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{solution}\mathrm{for}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{is}five.$