The number of solution(s) of the equation $sin x = 3^{x}$ in $[0, \frac{π}{2}]$ is

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Solution

The number of solution(s) of the equation $sin x = 3^{x}$ is equal to the number of point(s) of intersection of two curves $y = sin x$ and $y = 3^{x}$ in $[0, \frac{π}{2}] .$

$\begin{matrix} x & 0 & \frac{π}{2} sin x & 0 & 1 3^{x} & 1 & 3^{π / 2} \end{matrix}$

Clearly, in $[0, \frac{π}{2}], 3^{x}$ is always greater than $sin x .$
$∴$ Number of solutions $= 0$

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