Question

if x²+y²=18xy then prove that 2log (x-y)=4log 2+log x+log y​

Answer 1

Step-by-step explanation:

Given:x^2+y^2=18xy

RTP: 2log(x-y)=4 log 2+ log x+ log y

Proof: x^2+y^2= 18 xy ( given)

x^2+y^2-2 xy= 18 xy -2 xy ( subtract 2xy both sides)

(x-y)^2 = 16 xy ( since x^2+y^2-2xy= (x-y)^2

log (x-y)^2= log 16xy ( applying log both sides)

2 log (x- y) = log 16+ log x+ log y

= log 2^4+ log x+ log y

2 log ( x- y) = 4 log 2 + log x+ log y

hence proved....

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