Question

please answer fast.... (clads XI logarithm)

Answer 1

$Given : log( \frac{x + y}{5} ) = \frac{1}{2} (log x + log y)$

We know that log a + log b = log ab.

$log( \frac{x + y}{5} ) = \frac{1}{2} (log xy)$

$log( \frac{x + y}{5} ) = log(xy)^ \frac{1}{2}$

$(\frac{x + y}{5}) = (xy)^ \frac{1}{2}$

$( \frac{x + y}{5} ) = \sqrt{xy}$

$( \frac{x +y}{5} )^2 = (xy)$

$\frac{x^2 + y^2 + 2xy}{25} = xy$

x^2 + y^2 + 2xy = 25xy

x^2 + y^2 = 23xy

$\frac{x^2 + y^2}{xy} = 23$

$\frac{x^2}{xy} + \frac{y^2}{xy} =23$

$\frac{x}{y} + \frac{y}{x} = 23$


LHS = RHS.


Hope this helps!