Question

if log ( m+n/3) =1/2 (log m + log n ); show that : m/n + n/m=7​

Answer 1

Answer:

$log( \frac{m + n}{3} ) = \frac{1}{2}(log \: m+ log \: n)$

$2 log( \frac{m + n}{3} ) = log(m) + log(n)$

$log { (\frac{m + n}{3}) }^{2} = log(mn)$

$( \frac{m + n}{3})^{2} = mn$

${(m + n)}^{2} = 9mn \\ {m}^{2} + {n}^{2} + 2 mn= 9mn$

${m}^{2} + {n}^{2} = 9mn - 2mn \\ { m}^{2} + {n}^{2} = 7mn$

$\frac{ {m}^{2} + {n}^{2} }{mn} = 7$

$\frac{ {m}^{2} }{mn} + \frac{ {n}^{2} }{mn} = 7$

$\frac{m}{n} + \frac{n}{m} = 7$

Answer 2

Answer:

Step-by-step explanation: