Question

if ln x+y/2=1/2(lnx +lny) show that x=y

Answer 1

Steps :
1)
$ln( \frac{x + y}{2} ) = \frac{1}{2} (ln(x) + ln(y) ) \\ = > 2 ln( \frac{x + y}{2} ) = ln(x) + ln(y) \\ = > ln(( { \frac{x+y }{2}) }^{2} ) = ln(xy) \\ = > {(x + y)}^{2} = 4xy \\ = > {x}^{2} + 2xy + {y}^{2} = 4xy \\ = > {x}^{2} - 2xy + {y}^{2} = 0 \\ = > {(x - y)}^{2} = 0 \\ = > x = y$
Hence, proved √√

Answer 2

Answer:

Step-by-step explanation:

Steps :

1)

ln( \frac{x + y}{2} ) = \frac{1}{2} (ln(x) + ln(y) ) \\ = > 2 ln( \frac{x + y}{2} ) = ln(x) + ln(y) \\ = > ln(( { \frac{x+y }{2}) }^{2} ) = ln(xy) \\ = > {(x + y)}^{2} = 4xy \\ = > {x}^{2} + 2xy + {y}^{2} = 4xy \\ = > {x}^{2} - 2xy + {y}^{2} = 0 \\ = > {(x - y)}^{2} = 0 \\ = > x = y

Hence, proved √√