Question

log x+y/2= 1/2 (logx+ +logy)prove that x = y

Answer 1

$log( \frac{x + y}{2} ) = \frac{1}{2} (log(x) + log(y) ) \\ log( \frac{x + y}{2} ) = \frac{1}{2} log(xy)$
$log( \frac{x + y}{2} ) = { log(xy) }^{ \frac{1}{2} }$
criss cross log both the sides and you'll be left with
$\frac{x + y}{2} = {xy}^{ \frac{1}{2} } \\ ({ \frac{x + y}{2}) }^{2} = xy \\ \frac{ {x}^{2} + {y}^{2} + 2xy}{4} = xy \\ {x}^{2} + {y}^{2} + 2xy = 4xy \\ {x}^{2} + {y}^{2} = 4xy - 2xy \\ {x}^{2} + {y}^{2} = 2xy$
${x}^{2} + {y}^{2} - 2xy = 0 \\ {(x - y) }^{2} = 0$
now lets find the zeroes
x-y = 0
x = y a d similarly while fibding other again x = y

hence proved thay x is indeed equal to y.

Answer 2

Answer:

If log x+y/2 = 1/2(logx+logy) prove that x=y

Step-by-step explanation: