If a = 5^x, b = 5^y and a^y×b^x = 25 then prove that: xy =1

1 answer:

3 0

$a = {5}^{x} \\ b = {5}^{y} \\ {a}^{y} \times {b}^{y} = 25 \\ prove \: ( {5}^{x} )^{y} \times ( {5}^{y} ) ^{x} = 25 \\ {5}^{xy} \times {5}^{yx} = {5}^{2} \\ {5 }^{xy + yx} = 5^{2} \\ 5^{2xy} = {5}^{2} \\ is \: \: 2xy = 2 \\ xy = \frac{2}{2} \\ xy = 1$

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mamaluj [8]

Answer:

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julia-pushkina [17]

Answer:

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Luden [163]

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