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29 Jan 2021, 02:46
Kudos
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please help me:
a/b = 2/3
a^b = b^a
b-a = ?
a/b = 2/3
a^b = b^a
b-a = ?
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29 Jan 2021, 05:01
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iatii
if a = 2x then b = 3x
\(a^b = b^a\)
\((2x)^{3x} = (3x)^{2x}\)
i.e. \(x^{3x-2x} = \frac{3^{2x}}{2^{3x}} = \frac{9^x}{8^x}\)
i.e. \((8x)^x = 9^x\)
i.e. \(x = \frac{9}{8}\)
\(b-a = 3x - 2x = x = \frac{9}{8}\)
iatii
29 Jan 2021, 23:37
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a/b = 2/3
a = 2b/3
\(a^b = b^a\)
\(\frac{[2b}{3]}^b = b^\frac{2b}{3}\)
\(\frac{2b}{3} = b^\frac{2}{3}\)
\(\frac{2}{3} = b^\frac{-1}{3}\)
\(b^\frac{1}{3} = \frac{3}{2}\)
\(b = \frac{27}{8}\)
So, a = 9/4
b - a
= 27/8 - 9/4
= 27/8 - 18/8
= 9/8
Posted from my mobile device
a = 2b/3
\(a^b = b^a\)
\(\frac{[2b}{3]}^b = b^\frac{2b}{3}\)
\(\frac{2b}{3} = b^\frac{2}{3}\)
\(\frac{2}{3} = b^\frac{-1}{3}\)
\(b^\frac{1}{3} = \frac{3}{2}\)
\(b = \frac{27}{8}\)
So, a = 9/4
b - a
= 27/8 - 9/4
= 27/8 - 18/8
= 9/8
Posted from my mobile device
