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

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Answer 1 · 2018-07-20T17:32:03

Well we can write this as

${(\frac{2}{5})}^{x} + {(\frac{3}{5})}^{x} = 1$ $(2/5)^x+(3/5)^x=1$

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

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