log(x+y/3) = 1/2 (logx+logy), then the value of x/y +y/x is
Anonymous:
is it y/3
or whole term divided by 3
the answer is 7
it is ur mistake... becoz u didn't rply
on is it y/3 or whole term /3
I have edited my ans have a another look towards that
Answers
Answered by
3
HEYA!!
2× log{ ( x + y )/3 } = ( log x + log y )
log { ( x + y )² /9} = log x + log y
Becoz log aⁿ = n log a
log { ( x + y )² /9} = log ( xy )
Becoz log m + log n = log ( m × n )
( x + y )² = 9xy
x² + y² + 2xy = 9xy
x² + y² = 7xy
DIVIDE BOTH SIDES BY xy
x/y + y/x = 7
ANSWER IS 7
Answered by
1
log(x+y)/3=1/2(logx+logy)
log(x+y)/3=log(xy)^1/2......(loga+logb=logab and nloga =loga^n)
now,
on eliminating log from both sides
(x+y)/3=(xy)^1/2
[(x+y)/3]²=(xy)
(x+y)²/9=xy
x²+y²+2xy=9xy
x²+y²=9xy-2xy
x²+y²=7xy
x²/xy + y²/xy =7
x/y + y/x = 7
hope this helps
Similar questions