Question

If $\log 2=0.3010$ and $\log 3=0.4771$, then find the value of $\log \sqrt{24}$.

• A. $0.69005$
• B. $0.6905$
• C. $1.695$
• D. $1.3801$

Answer 1

The correct option is A $0.69005$

$\log \sqrt{24}=\log (24{)}^{\frac{1}{2}}$

$=\frac{1}{2}\log \left(24\right)$

$=\frac{1}{2}\log (8\times 3)$

$=\frac{1}{2}\log (2\times 2\times 2\times 3)$

$=\frac{1}{2}(\log 2+\log 2+\log 2+\log 3)$

$=\frac{1}{2}(0.3010+0.3010+0.3010+0.4771)$

$=\frac{1}{2}\left(1.3801\right)$

$=0.69005$