Question

Express log $\frac{3\sqrt{a^2}}{b^5\sqrt{c}}$ in terms of log a log b and log c.

• A.
  $\frac{2}{3}loga-5logb+\frac{1}{2}logc$
• B. $\frac{3}{2}loga-5logb+\frac{1}{2}logc$
• C. $\frac{2}{3}loga+5logb-\frac{1}{2}logc$
• D. $\frac{3}{2}loga+5logb+\frac{1}{2}logc$

Answer 1

The correct option is D $\frac{3}{2}loga+5logb+\frac{1}{2}logc$

$\frac{3\sqrt{a^2}}{b^5\sqrt{c}}$
=log $a^{\frac{3}{2}}$ - logb${}^5$ + log $\sqrt{c}$
= $\frac{3}{2}$ log a - 5 log b + $\frac{1}{2}$ log c