Question

Find the number of solutions of equation $2^x+3^x+4^x-5^x=0$ .

Answer 1

$2^x+3^x+4^x-5^x=0$

$\Rightarrow 2^x+3^x+4^x=5^x$

$\Rightarrow {\left(\frac{2}{5}\right)}^x+{\left(\frac{3}{5}\right)}^x+{\left(\frac{4}{5}\right)}^x=1$

Now the number of solutions of the equation is equal to number of times.

From the graph, equation has only one solution.