Question

If log(x+y/3)=1/2(logx+logythen find the value of x/y+y/x

Answer 1

★ LOGARITHMIC EQUATIONS ★

☣ LOG ( x / 3 + y / 3 )= 1/2 ( log x + log y )

☣ LOG ( x / 3 + y / 3 )= 1/2 ( logxy )

☣ LOG ( x / 3 + y / 3 )= log √xy

☣ So, Reducing base to logaritms ...

☣ we obtain ,

☣ x / 3 + y / 3 = √xy

☣ x + y = 3 √xy

☣ ( x + y )² = 9 xy ... ( i )

☣ NOW , Required value to obtain is aslike ...

☣ x / y + y / x =

☣ x ² ⁺ y ² / xy =

☣ ( x + y ) ² - 2xy / xy =

☣ By using equation (i)

☣ 9xy - 2xy / xy =

☣ 7xy / xy =

☣ 7

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Answer 2

Applying basic logarithm rules we can write given equation as



****(x+y) /3=under root xy------(1)

****we have to solve (x/y) +(y/x) that is (x²+y²)/xy

****X²+Y² can be written as (x+y) ²-2xy

****And we know that x+y=3under root xy(from equation 1)

****So,,,( (3under root xy) ²-2xy)/xy
Which reduces to 7
¦¦¦¦¦¦¦¦Therefore your answer is 7¦¦¦¦¦¦¦¦