if log (x+y)/7=1/2(logx+logy) prove that x/y+y/x=47

Question

hartnn · Answer

2 log [(x+y)/7]  = log x + log y 

you know logarithm properties ?

hartnn · Answer

how will you simplify log x + log y ?

hartnn · Answer

no? / yes? / just give me answer?

anonymous · Answer

hi are you speaking to me?

hartnn · Answer

hey dane, yes :)
since you asked that question, i wanted to know whether you know some logarithm properties which will help us solve this problem :)

anonymous · Answer

cool !!!:) yes i know the logarithm properties

hartnn · Answer

nice , how will you simplify 
log x + log y 
?

anonymous · Answer

log xy?

hartnn · Answer

correct! 

now 
$\log a^b = b \log a$

so if i had [b log a], i could write it as $\log a^b$
right ?

similarly how will i write 
2 log [(x+y)/7] as ?

anonymous · Answer

log(x+y/7)^2

hartnn · Answer

oh wow, you're good at logarithms :)

$\log [(x+y)/7]^2 = \log xy$

so we can simply write 
$ [(x+y)/7]^2 = xy$ 

isn't it ?
can you simplify that further ?

hartnn · Answer

expand the left side

hartnn · Answer

everything after this is purely algebraic :)

anonymous · Answer

can you help me with the key to type square on the keyboard instead of typing ^

anonymous · Answer

thanks a million god bless you

anonymous · Answer

you gone?

hartnn · Answer

just went to help other users too :)
and you're most welcome ^_^

type 

$x^2 $

as
`$x^2 $`

anonymous · Answer

so kind of you !! can i ask another?

hartnn · Answer

sure :)
ask as many as you want :)

hartnn · Answer

since you're new here,
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $

usukidoll · Answer

@hartnn !!! yay

anonymous · Answer

thanks