Question

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

Answer 1

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

Answer 2

Given :  x² + y² = 25xy

To Find :  prove that 2 log(x+y) = 3log3 + logx + logy.

Solution:

x² + y² = 25xy

Add 2xy both sides

=> x² + y² + 2xy = 25xy + 2xy

=> ( x + y)² = 27 xy

Taking long both sides

=> log (( x + y)²) = log (27xy)

log aⁿ =  n log a

log (abc) = log a + log b + log c

=> 2 log (x + y) = log 27 + log x + log y

=> 2 log (x + y) = log 3³ + log x + log y

=> 2 log (x + y) = 3log3  + log x + log y

QED

Hence Proved

Learn More:

y=log(ab) z=log(a²-b²).

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[ab]; y=log [a+b] ; z= log [a2 - b2 ]

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