Question

If x²+y²=23xy then the value of log(x+y/5)=

Answer 1

Answer:

Given:

x

2

+y

2

=23xy,

So, the above equation can be written as

x

2

+y

2

=25xy−2xy

x

2

+y

2

+2xy=25xy

(x+y)

2

=25xy

(x+y)

2

/25=xy

Now by taking log on both sides, we get

log[(x+y)

2

]/25=logxy

log[(x+y)/5]

2

=logx+logy

2log[(x+y)/5]=logx+logy

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

Hence proved

Answer 2

Answer:

Given:

x² +y ² =23xy

⠀

To find :

log(x+y/5)= ??

so the equation can be written as..

x ² +y ²

=25xy−2xy

x ² +y ² +2xy=25xy

(x+y) ² =25xy

(x+y) ² /25=xy

now by taking log on both sides..

we get,

log [(x+y) ² ] /25=log x y

log [(x+y)/5]² =log x+log y

$2log \:[(x+y)/5]\: =log x+log y$

$\:log\:(x+y)/5=1/2\:(log x+log y)$