Question

Express the $\log \left(\frac{\sqrt{a^3}}{c^5{b}^2}\right)$ in terms of $\log a,\log b,$ and $\log c$.

• A. $\frac{3}{2}\log a-5\log c-2\log b$
• B. $3\log a-5\log c-2\log b$
• C. $\frac{3}{2}\log a-5\log c-\frac{2}{3}\log b$
• D. $\frac{3}{2}\log a-5\log c-\log b$

Answer 1

Answer: (A)

$\frac{3}{2}\log a-5\log c-2\log b$

We know that $\log AB=\log A+\log B$

And $\log \frac{A}{B}=\log A-\log B$

Also, $\log a^b=b\log a$

So, $\log \left(\frac{\sqrt{a^3}}{c^5{b}^2}\right)=\log \sqrt{a^3}-\log c^5{b}^2$

$=\frac{3}{2}\log a-5\log c-2\log b$