Question

The number of solutions of the equation $2^x=x{5}^x$ is

Answer 1

$2^x=x{5}^x\Rightarrow \frac{2^x}{5^x}=x\Rightarrow {\left(\frac{2}{5}\right)}^x=x$

Graph of $y={\left(\frac{2}{5}\right)}^x$ and $y=x$
We will draw the graph of $a^x$ where $0<a<1$


Hence, only one solution is possible.