Question

If ${\log }_{10}8=0.90$ and $\log \sqrt{32}$ = $\frac{m}{4}$, then the value of $m$ is equal to

• A. $43$
• B. $8$
• C. $3$
• D. $6$

Answer 1

Answer: (C)

$3$

Goven, ${\log }_{10}8=0.9$

$\Rightarrow {\log }_{10}{2}^3=0.9$
$\Rightarrow 3{\log }_{10}=0.9$ (Using $\log a^b=b\log a$)
$\Rightarrow {\log }_{10}2=0.3$
Now, ${\log }_{10}\sqrt{32}=\frac{5}{2}{\log }_{10}2=2.5\times 0.3=0.75=\frac{3}{4}$

$\Rightarrow m=3$.