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Find how many solutions are there in 2^x+3^x+4^x-5^x=0

Find how many solutions are there in 2^x+3^x+4^x-5^x=0

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago

one solution.

let f(x) = 5^x
g(x) = 2^x+3^x+4^x
the exponential functions are monotonic. 
sum of monotonic functions is monotonic.

for x=0 
we have f(0) = 1

g(0) = 3 
g(x) is above f(x) 
for x=3

f(3) = 125
g(3) = 8+27+64 = 99
f(3) is above g(3)
Hence there exists a cross over point in (0,3).

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