Question

Find the number of solutions of 2^x+3^x+4^x-5^x=0. Correct answer will be marked brainliest. Please don't spam.​

Answer 1

Answer:

2 x +3 x +4 x−5 x =0

⇒2 x +3 x +4 x =5 x

⇒(

5

2

)

x

+(

5

3

)

x

+(

5

4

)

x

=1

Answer 2

$2^x+3^x+4^x-5^x=0 \\ {2}^{x} + {3}^{x} + {4}^{x} = {5}^{x} \\ ( \frac{2}{5} ){}^{x} + ( \frac{3}{5} {}^{} ) {}^{x} + ( \frac{4}{5} ) {}^{x} = 1$

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

From the graph, equation has only one solution.