Question

Calculate to six decimal places the value of $(330÷49{)}^4\sqrt[3]{322\times 70};$ given $\log 2,\log 3,\log 7;$ also $\log 11=1^{.}0413927,$ and $\log {17814}^{.}1516=4^{.}2507651.$

Answer 1

Let $y=(330÷49{)}^4÷\sqrt[3]{322\times 70}$

$\Rightarrow \log y=4\log 330-4\log 49-\frac{1}{3}\log 22-\frac{1}{3}\log 70$

$\Rightarrow \log y=4(1+\log 3+\log 11)-8\log 7-\frac{1}{3}(\log 2+\log 11)-\frac{1}{3}(\log 7+1)$

$\Rightarrow \log y=2.2507651$

$\Rightarrow y=178.141516$