Question

x square +y square=23xy,prove that log x+y/5=1/2(log x+log y)

Answer 1

Heya user
Here is your answer !!

x^2 + y^2 = 23xy
=> x^2 + y^2 + 2xy = 25xy
=> ( x + y )^2 = 25xy
=> x + y = 5 (xy)^1/2

So , taking log both sides ,
log ( x + y ) = log { 5 (xy)^1/2 }
=> log ( x + y ) = log 5 + log (xy)^1/2
=> log ( x + y ) - log 5 = 1/2 log xy
=> log ( x + y / 5 ) = 1/2 log xy [ Proved ]

Hope it helps !!

Answer 2

Hey there!

x²+y²=23xy

Adding 2xy on both sides.

x²+y²+2xy =25xy
(x+y)² = (25xy)
(x+y) = √25xy
(x+y) = 5√xy
(x+y)/5 = √xy

Applying logarithm on both sides :)

log ( x+y)/5 = log√xy
log( x+y)/5 = 1/2 ( logxy)
log(x+y)/5 = 1/2(logx + logy )

Hence proved!