Jika [tex]x=\displaystyle ^2\log\left ( \frac{3^{31}+3^{32}}{3^{32}-3^{31}} \right )[/tex] dan [tex]y=2~\displaystyle ^3\log\left ( \frac{2^{21}+2^{22}}{2^{22}-2^{21}} \right )[/tex] tentukan nilai dari [tex]\displaystyle \frac{x^x+y^y}{y^x-x^y}[/tex]
Verified answer
ALjabar
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x = ²log ((3³¹ + 3³²)/(3³² - 3³¹))
x = ²log (3³¹(1 + 3) / 3³¹(3 - 1))
x = ²log (4/2)
x = 1
y = 2 ³log ((2²¹ + 2²²)/(2²² - 2²¹))
y = 2 ³log (2²¹(1 + 2) / 2²¹(2 - 1))
y = 2 ³log (3/1)
y = 2
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[tex] \sf{\frac{x^x+y^y}{y^x-x^y}} \\ \\ \sf{ = \: \frac{ {1}^{1} \: + \: {2}^{2} }{ {2}^{1} \: - \: {1}^{2} } } \\ \\ \sf{ = \: 5}[/tex]