Question

plzz solve 21st question ..

Answer 1

Final Answer : D)
$\frac{xy}{x + y}$

Steps:
1) Let
${4}^{x} = {5}^{y} = {20}^{z} = k$
=>
$x ln(4) = y ln(5) = z ln(20) = ln(k) \\ = > x ln(4) = ln(k) \\ = > ln(4) = \frac{ ln(k) }{x} - - - (1) \\ = > y ln(5) = ln(k) \\ = > ln(5) = \frac{ ln(k) }{y} - - - - (2) \\ = > ln(20) = \frac{ ln(k) }{z} - - - (3)$

3) We know that
$ln(20) = ln(4) + ln(5) \\ = > \frac{ ln(k) }{z} = \frac{ ln(k) }{y} + \frac{ ln(k) }{x} \\ = > \frac{1}{z} = \frac{1}{y} + \frac{1}{x} \\ = > z = \frac{xy}{x + y}$