Question

if x×x+y×y=7xy show that 2log(x×y)=log x+log y+2 log3​

Answer 1

x² + y² = 7xy (given)

Add 2xy in both sides of above equation.

→ x² + y² + 2xy = 7xy + 2xy = 9xy

So (x + y)² = 9xy (Consider logarithm on both sides)

We get log (x + y)² = log 9xy

→ 2log (x + y)= log 9 + log x + log y

= log x + log y + log 3²

= log x + log y + 2 log 3

2 log (x + y) = log x + log y + 2 log 3

Hence proved.