Question

log(xy^3) = 1, log(yx^2) = 1, Find log(xy)

Answer 1

Answer:

We have,

log(

3

x+y

)=

2

1

(logx+logy)

⇒log(

3

x+y

)=(logx)

2

1

+(logy)

2

1

⇒log(

3

x+y

)=log

x

+log

y

⇒log(

3

x+y

)=log

x

y

(

3

x+y

)=

xy

x+y=3

xy

On squaring both side and we get,

(x+y)

2

=9xy

⇒x

2

+y

2

+2xy=9xy

⇒x

2

+y

2

=9xy−2xy

⇒x

2

+y

2

=7xy

On divide both side by xy and we get,

xy

x

2

+y

2

=

xy

7xy

⇒

y

x

+

x

y

=7

Hence, this is the answer.

Step-by-step explanation:

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