Question

m/n + n/m =14 show that. log(m+n/4)=1/2 (log m+log n)​

Answer 1

Step-by-step explanation:

m/n+n/m=14

${m}^{2} + {n}^{2} = 14mn$

$m ^{2} + {n}^{2} + 2mn = 16mn$

adding 2mn on both sides

${(m + n)}^{2} = 16mn$

applying log on both sides

$log(x + y)^{2} = log(16mn)$

$log(x + y)^{2} = log( {4}^{2} ) + log(m) + log(n)$

$log(m + n)^{2} - log( {4}^{2} ) = log(m) + log(n)$

$log( \frac{ {(m + n)}^{2} }{ {4}^{2} } ) = log(m) + log(n)$

$2 log( \frac{m + n}{4} ) = log(m) + log(n)$

$log( \frac{m + n}{4} ) = \frac{1}{2} ( log(m) + log(n) )$

hence proved