Question

Given $\log 2={}^{.}3010300,\log 3={}^{.}4771213,\log 7={}^{.}8450980,$ find the value of
$\log \sqrt[4]{4{}^{.}0105}.$

Answer 1

$\log \sqrt[4]{40.0105}=\frac{1}{4}(\log 105-4)$

$=\frac{1}{4}(\log (7\times 3\times 5)-4)$

$=\frac{1}{4}(\log 7+\log 3+\log 5-4)$

$=\frac{1}{4}(\log 7+\log 3+\log \left(\frac{10}{2}\right)-4)$

$=\frac{1}{4}(\log 7+\log 3+1-\log 2-4)$

$=-0.494702675$