Question

The value of $(\log a{)}^2-(\log b{)}^2$ is

• A. $\log \left(\frac{b}{a}\right).\log \left(ab\right)$
• B. $\log \left(\frac{a}{b}\right).\log b$
• C. $\log \left(\frac{a}{b}\right).\log a$
• D. $\log \left(\frac{a}{b}\right).\log \left(ab\right)$

Answer 1

Answer: (D)

$\log \left(\frac{a}{b}\right).\log \left(ab\right)$

$x=(loga{)}^2-(logb{)}^2$
$\therefore x=(loga+logb)(loga-logb)$ {$a^2-b^2=(a+b)(a-b)$}
$\therefore x=log\left(\frac{a}{b}\right).log(a.b)$ (Property of logarithm)