Question

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

• A. $x=70$ and $y=1$
• B. $x=40$ and $y=7$
• C. $x=10$ and $y=3$
• D. $x=50$ and $y=2$

Answer 1

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

$\log x+\log y=2...\left(i\right)\log x-\log y+2\log 2=2...\left(ii\right)\text{Subtracting eq(ii) from eq(i) we get}2\log y-2\log 2=02\log y=2\log 2\therefore y=2Now,\log xy=2\text{Assuming base 10}\therefore {\log }_{10}2x={\log }_{10}{10}^2{\log }_{10}2x={\log }_{10}100x=50$