Question

Given ${\log }_{10}x=2a$ and ${\log }_{10}y=\frac{b}{2}$

If ${\log }_{10}\left(P\right)=3a-2b$, then P in terms of $x$ and $y$ is

• A. $P=\frac{x^{\frac{6}{7}}}{y^2}$
• B. $P=\frac{x^{\frac{13}{6}}}{y^7}$
• C. $P=\frac{x^{\frac{3}{2}}}{y^4}$
• D. $P=\frac{x^{\frac{1}{2}}}{y^3}$

Answer 1

Answer: (C)

$P=\frac{x^{\frac{3}{2}}}{y^4}$

${\log }_{10}x=2a{\log }_{10}y=\frac{b}{2}3a=\frac{3}{2}\times 2a=\frac{3}{2}{\log }_{10}x2b=4\times \frac{b}{2}=4{\log }_{10}y{\log }_{10}P=3a-2b=\frac{3}{2}{\log }_{10}x-4{\log }_{10}y{\log }_{10}P={\log }_{10}\frac{x^{\frac{3}{2}}}{y^4}\text{Removing log}P=\frac{x^{\frac{2}{3}}}{y^4}$