Question

If $\frac{\log x}{\log y}=\frac{3}{2}$ and $\log \left(xy\right)=5$, then the value of $x$ is equal to

• A. $1000$
• B. $2160$
• C. $1080$
• D. $1220$

Answer 1

The correct option is A $1000$

$\log xy=5...\left(i\right)\log x+\log y=5...\text{(Multiplication rule)}\frac{\log x}{\log y}=\frac{3}{2}...\left(ii\right)\therefore \log x=\frac{3}{2}\log ySo....\frac{3}{2}\log y+\log y=5\text{Assuming base 10}\frac{5}{2}{\log }_{10}y=5{\log }_{10}10\log y^{\frac{5}{2}}=\log {10}^5\therefore y={10}^2=100\log x=\frac{3}{2}\log y\log x=\frac{3}{2}\log {10}^2=\log {10}^3\therefore x=1000$