Question

If $x^2+y^2$ = 10xy, then$2log(x+y)$ =

• A. $\log 12+\log x+\log y$
• B. $\log 4+\log x+\log y$
• C. $\log 8+\log xy$
• D. $\log 10xy$

Answer 1

Answer: (A)

$\log 12+\log x+\log y$

Given,

$x^2+y^2=10xy$

Concept used:

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

Apply the above concept, we get

$(x+y{)}^2-2xy=10xy$

$(x+y{)}^2=12xy$

On taking logarithm both sides, we get

$\log (x+y{)}^2=\log (12xy)$

Concept used:

$\log \left(ab\right)=\log a+\log b$

Apply the above concept, we get

$2\log (x+y)=\log 12+\log x+\log y$

Hence, option $\left(a\right)$ is the correct answer.