Question

if 2 log (x+y/4)=logx+logy,then find the value of x/y+y/x​

Answer 1

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Answer 2

❥︎Question :-

$\bf \:If \: 2 log(\dfrac{x + y}{4} ) = logx + logy$

$\bf \:find \: the \: value \: of \dfrac{x}{y} + \dfrac{y}{x}$

❥︎Answer

❥︎Properties of logarithms :-

$\bf \:logx + logy = logxy$

$\bf \:logx - logy = log\dfrac{x}{y}$

$\bf \:log {x}^{y} = ylogx$

❥︎Solution :-

$\bf \:2 log(\dfrac{x + y}{4} ) = logx + logy$

$\bf\implies \: log( {\dfrac{x + y}{4}})^{2} = logxy$

$\bf\implies \:\bf ({\dfrac{x + y}{4}})^{2} = xy$

$\bf\implies \:\dfrac{ {x}^{2} + {y}^{2} + 2xy }{16} = xy$

$\bf\implies \: {x}^{2} + {y}^{2} + 2xy = 16xy$

$\bf\implies \: {x}^{2} + {y}^{2} = 14xy$

$\bf\implies \:\dfrac{ {x}^{2} + {y}^{2} }{xy} = 14$

$\bf\implies \:\dfrac{x}{y} + \dfrac{y}{x} = 14$