Question

If $2\log y-\log x-3=0$ express $x$ in terms of $y.$

• A. $x^2=1000y$
• B. $x^2=\frac{y^2}{e^3}$
• C. $y^2=\frac{x}{1000}$
• D. $y^2=1000x$

Answer 1

The correct option is B $x^2=\frac{y^2}{e^3}$

Given: $2\log y-\log x-3=0$

$\log y^2-\log x-3\log e=0$.......$(\log e=1)$

$\log y^2-\log x-\log e^3=0$

$\log x=\log y^2-\log e^3=\log \left(\frac{y^2}{e^3}\right)$

$x=\frac{y^2}{e^3}$