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

Text Solution

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`2^(x)+3^(x)+4^(x)=0`
`or 2^(x)+3^(x)+4^(x) = 5^(x)`
` or (2/5)^(x)+(3/5)^(x)+(4/5)^(x) = 1`
Now the number of solutions of the equation is equal to number of times, graphs of
`y = (2/5)^(x) + (3/5)^(x)+(4/5)^(x) and y = 1` intersect.

From the graph, equation has only one solution , `x_(0)`.
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