$2^x$ + $3^x$ = $5^x$ find all possible values of x?

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Answer 1 · 2018-07-20T17:32:03

Well we can write this as

$(2/5)^x+(3/5)^x=1$

The LHS is strictly decreasing, and there is a unique solution which is $x=1$

2^x2^x+3^x3^x=5^x5^x find all possible values of x?