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Arithmetic Progression

If x∧ 2+y∧ 2=...

Question

If x^2+y^2=25xy then prove that 2log(x+y)=3log3+log x+log y

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Solution

x²+y²=25xy
adding 2xy on both sides
x²+y²+2xy=27xy
[x+y]²=27xy
taking log on both sides
log[x+y]²=log27xy

log(abc)= log a+ log b+ log c
Log27xy=log(27×x×y)
=Log(3³×x×y)
=Log 3³ + log x+ log y
Log[x+y]²= 2 log [x+y]
Now,

Log[x+y]²= log 27xy

2log[x+y]=log3³+log x+log y
2 log[x+y]=3log3+logx+logy

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Similar questions

x^{2} + y^{2} = 25 x y,

then prove that

2 log (x + y) = 3 log 3 + log x + log y .

x^{2} + y^{2} - 25 x y, t h e n p r o v e 2 l o g (x + y) = 3 l o g 3 + l o g x + l o g y

x^{2} + y^{2} = 25 x y

2 l o g (x + y) = 3 l o g 3 + l o g x + l o g y

log \frac{x + y}{2} = \frac{1}{2} (log x + log y)

x = y

x^{2} + y^{2} = 7 x y

2 log (x + y) = log x + log y + 2 log 3

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