Question

If Log (x+y)/3=1/2(logx+log4) find the volume x/y+y/x

Answer 1

$\textbf{Answer}$

7
OR

343

Depend on question


$\textbf{Correction}$

or it is may be Y not 4
it is Value in place of volume (?)


$\textbf{Otherwise}$

${ (\frac{x}{y} + \frac{y}{x}) }^{3}$


$\textbf{Step-By-Step Solution}$


$\textbf{Step.1}$

$log \frac{x + y}{3} = \frac{1}{2} log(x) + log(y)$


$\textbf{Step.2}$

$2( log( \frac{x + y}{3} ) ) = log(x) + log(y)$


$\textbf{Step.3}$

$\textbf{Using log theorm}$

$n log(x) = log( {x}^{n} )$
$log( { (\frac{x + y}{3} )}^{2} ) = log(x )+ log(y)$


$\textbf{Step.4}$

$log(x) + log(y) = log(xy)$

$\textbf{Therefore}$

$log( {( \frac{x + y}{3}) }^{2} ) = log(xy)$


$\textbf{Step.5}$

Cancel log both side

${ \: (\frac{x + y}{3} )}^{2} = xy$


$\textbf{Step.6}$

$\frac{ {(x + y)}^{2} }{9} = xy$


$\textbf{Step.7}$

${x}^{2} + {y}^{2} + 2xy = 9xy$


$\textbf{Step.8}$

${x }^{2} + {y}^{2} = 7xy$


$\textbf{Step.9}$

Divide the all by $\textbf{xy}$

$\frac{x}{y} + \frac{y}{x} = 7$

Now if your questions is cube of this value

then , ans is

$= { (\frac{x}{y} + \frac{y}{x}) }^{3} = {7}^{3}$

${( \frac{x}{y} + \frac{y}{x} )}^{3} = 343$