Question

jika :
x = ²log((3³¹ + 3³²)/(3³² - 3³¹)
y = 2³log(2²¹ + 2²²)/(2²² - 2²¹)
tentukan :
(x^x + y^y)/(y^y + x^y)
[tex] \\ [/tex]
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Answer 1

Verified answer

Jawab:

1

Penjelasan dengan langkah-langkah:

[tex]\displaystyle x=^2\log \left ( \frac{3^{31}+3^{32}}{3^{32}-3^{31}} \right )\\=^2\log \left ( \frac{3^{31}+3^{31+1}}{3^{31+1}-3^{31}} \right )\\=^2\log \left ( \frac{3^{31}+3^{31}(3)}{3^{31}(3)-3^{31}} \right )\\=^2\log \left [ \frac{3^{31}(1+3)}{3^{31}(3-1)} \right ]\\=1[/tex]

[tex]\displaystyle y=2~^3\log \left ( \frac{2^{21}+2^{22}}{2^{22}-2^{21}} \right )\\=2~^3\log \left ( \frac{2^{21}+2^{21+1}}{2^{21+1}-2^{21}} \right )\\=2~^3\log \left ( \frac{2^{21}+2^{21}(2)}{2^{21}(2)-2^{21}} \right )\\=2~^3\log \left [ \frac{2^{21}(1+2)}{2^{21}(2-1)} \right ]\\=2[/tex]

[tex]\displaystyle \frac{x^x+y^y}{y^y+x^y}\\=\frac{1^1+2^2}{2^2+1^2}\\=\frac{5}{5}\\=1[/tex]