log10{(x + y)/3} = (1/2)(log10x + log10y) হলে (x/y) + (y/x) এর মান কত?

প্রশ্ন: log₁₀{(x + y)/3} = (1/2)(log₁₀x + log₁₀y) হলে (x/y) + (y/x) এর মান কত?

সমাধান: 
 log₁₀{(x + y)/3} = (1/2)(log₁₀x + log₁₀y) 
⇒ log₁₀{(x + y)/3} =(1/2)log₁₀(xy)
⇒ log₁₀{(x + y)/3} =log₁₀(xy)^(1/2)
⇒ (x + y)/3 = (xy)^(1/2)
⇒ {(x + y)/3}² = {(xy)^(1/2)}²
⇒(x + y)²/9 = xy
⇒ x² + 2xy + y² = 9xy 
 ⇒ x² + y² = 9xy - 2xy 
⇒ x² + y² = 7xy 
⇒ x²/xy + y²/xy = 7
(x/y) + (y/x) = 7