Question

If $x>0$ and $y>0$, then the values of $x$ and $y$ from $\log xy=\log \frac{x}{y}+2\log 2=2$ are

• A. $x=10$ and $y=4$
• B. $x=50$ and $y=2$
• C. $x=30$ and $y=7$
• D. $x=40$ and $y=1$

Answer 1

The correct option is B $x=50$ and $y=2$

$\log x+\log y=\log x-\log y+\log 4=0\log y=-\log y+\log 4...\text{(Canceling log x on both sides)}2\log y=\log 4\log y^2=\log 2^{2}y=2\log 2x=2\text{Assuming base 10}2x={10}^{2}x=50$