If log (x+y/3) = 1/3 (log x + log y) then find the value of x/y + y/x ..pls help i have exam
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Step-by-step explanation:
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.
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