Question

If $x^2+y^2=7xy$, then which of the following are true?

• A. $2log\left(xy\right)=log7+logx+logy$
• B. $2log(x+y)=2log3+logx+logy$
• C. $log(x+y)=log3+\frac{1}{2}log\left(xy\right)$
• D. Both (b) and (c)

Answer 1

Answer: (D)

Both (b) and (c)

We have,

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

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

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

On takin $log$ both sides, we get

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

We know that

$log{m}^n=nlogm$

$log\left(abc\right)=loga+logb+logc$

Therefore,

$2log(x+y)=log9+logx+logy$

$2log(x+y)=log{3}^2+logx+logy$

$2log(x+y)=2log3+logx+logy$

$log(x+y)=log3+\frac{1}{2}[logx+logy]$

$log(x+y)=log3+\frac{1}{2}\left[logxy\right]$

Hence, this is the answer.