Question

Given:$\log 2=0.3010$ and $\log 3=0.4771$, find the value of $\log \sqrt{18}$.

Answer 1

Given $\log 2=0.3010$ and $\log 3=0.4771$

$\log \sqrt{18}=\log {18}^{\frac{1}{2}}=\frac{1}{2}\log 18$

$=\frac{1}{2}\left[\log \right(2\times 3^2\left)\right]$

$=\frac{1}{2}[\log 2+\log 3^2]$

$=\frac{1}{2}[\log 2+2\log 3]$

Substituting the values

$=\frac{1}{2}[0.3010+2\times 0.4771]$

$=\frac{1}{2}[0.3010+0.9542]$

$=\frac{1}{2}\left[1.2552\right]$

$=0.6276$