Question

Given $\log 2={}^{.}3010300,\log 3={}^{.}4771213,\log 7={}^{.}8450980,$ find the value of
$\log \sqrt{\frac{35}{27}}.$

Answer 1

$\log \left(\sqrt{\frac{35}{27}}\right)=\frac{1}{2}(\log \left(35\right)-\log \left(27\right))$

$=\frac{1}{2}(\log 7\times 5-\log 3+\log 3^3)$

$=\frac{1}{2}(\log 7+\log \left(\frac{10}{2}\right)-3\log 3)$

$=\frac{1}{2}(\log 7+1-\log 2-3\log 3)=0.05635205$