Question

if log(x+y/3)=1/2(log x+log y) than find the value of x/y+y/x​

Answer 1

Step-by-step explanation:

A class of children make paper chain decorations. They make the following lengths:1)15 chains are ⅖ of a metre long.2)15 chains are ½ a metre long.

Write two methods for finding the total length of the paper chains.Also,Find the total length and write it as a mixed number.

Answer 2

Step-by-step explanation:

$log [ ( x + y )/3] = 1/2 ( logx + logy)</p><p></p><p>2× log[ ( x + y )/3 ] = log x + log y</p><p></p><p>log [ ( x + y ) / 3 ]^2 = log xy</p><p></p><p>{ since i ) n log a = log a^n</p><p></p><p>ii ) log a + log b = log ab }</p><p></p><p>Remove log bothsides,</p><p></p><p>[ ( x + y ) / 3 ]^2 = xy</p><p></p><p>( x + y )^2 / 3^2 = xy</p><p></p><p>x^2 + y^2 + 2xy = 9xy</p><p></p><p>x^2 + y^2 = 9xy - 2xy</p><p></p><p>x^2 + y^2 = 7xy</p><p></p><p>Divide each term with xy</p><p></p><p>x^2 / xy + y^2 / xy = 7xy / xy</p><p></p><p>x / y + y / x = 7</p><p></p><p></p><p></p><p>$