Question

If log(x+y/2) = 1/2(log x+log y) show that x=y​

Answer 1

Answer:

$given \: that -$

Log(x+y/2) = 1/2(log x+ log y)

$to \: prove -$

x = y

$giving \: answer -$

log(

6

x+y

)=

2

1

(logx+logy)

⇒2log(

6

x+y

)=(logx+logy)

⇒log(

6

x+y

)

2

=(logx+logy)

⇒log(

6

x+y

)

2

=logxy

⇒(

6

x+y

)

2

=xy

⇒(x+y)

2

=36xy

⇒x

2

+y

2

+2xy=36xy

⇒x

2

+y

2

=34xy

⇒

xy

x

2

+y

2

=34

⇒

xy

x

2

+

xy

y

2

=34

⇒

y

x

+

x

y

=34