Question

Given ${\log }_{10}x=a,{\log }_{10}y=b$

If ${\log }_{10}P=2a-b$; express $P$ in terms of $x$ and $y$.

• A. $\frac{x^2}{y}$
• B. $x^{2}y$
• C. $\frac{y^2}{x}$
• D. $x{y}^2$

Answer 1

The correct option is A $\frac{x^2}{y}$

${\log }_{10}P=2a-b$

${\log }_{10}P=2{\log }_{10}x-{\log }_{10}y$

${\log }_{10}P={\log }_{10}{x}^2-{\log }_{10}y$

${\log }_{10}P={\log }_{10}\left(\frac{x^2}{y}\right)$

$\therefore P=\frac{x^2}{y}$