Question

x²+y²=6xy prove that 2log(x-y)=2log2+logx+logy

Answer 1

Hi ,

It is given that ,

x² + y² = 6xy

Subtract 2xy both sides of the

equation,

x² + y² - 2xy = 6xy - 2xy

( x - y )² = 4xy

( x - y )² = 2²xy

Take log both sides of the equation,

log ( x - y )² = log ( 2²xy )

2 log ( x - y ) = log 2² + logx + logy

[ Since 1 ) log a^n = n log a

2 ) log ab = log a + log b ]

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

Hence , proved .

I hope this helps you.

: )

Answer 2

HELLO DEAR,

given that:-

x² + y² = 6xy
[ subtracting "2xy" both side]

x² + y² - 2xy = 6xy - 2xy

(x - y)² = 4xy


(x - y)² = 2² × x × y

[taking log both side by property of log , loga^b = b × loga ] and [ log(a × b) = loga × logb]


we get,

2log(x - y) = 2 × log² + logx + logy




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