Question

If $x^2+y^2=25xy,$then prove that $2\log (x+y)=3\log 3+\log x+\log y.$

Answer 1

We have,

$x^2+y^2=25xy$

$x^2+y^2+2xy=25xy+2xy$

$(x+y{)}^2=27xy$

On taking logarithm, we get

$\log (x+y{)}^2=\log (27xy)$

$2\log (x+y)=\log 27+\log x+\log y$ $\because (\log m^n=n\log m)and(\log mn=\log m+\log n)$

$2\log (x+y)=\log 3^3+\log x+\log y$

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

Hence, proved.