Question

Evaluate:
(i) $816.3\times 37.42$
(ii) $816.3÷37.42$
(iii) $0.000645\times 82.3$
(iv) $0.3421÷0.09782$
(v) ${\left(50.49\right)}^5$
(vi) $\sqrt[3]{3561.4}$
(vii) $\frac{175.23\times 22.159}{1828.56}$
(viii) $\frac{\sqrt[3]{328}\times \sqrt[5]{5729}}{\sqrt{46.35}}$
(ix) $\frac{{\left(76.25\right)}^3\times \sqrt[3]{31.928}}{{\left(42.75\right)}^5\times 0.04623}$
(x) $\sqrt[3]{3\frac{0.7214\times 20.37}{69.8}}$
(xi) ${\log }_{9}63.28$
(x) ${\log }_{3}7$

Answer 1

$i)$ $y=816.3\times 37.42\log y=\log 816.3+\log 37.42\log y=4.48499y=anti\log \left(4.4849\right)y=30542.2$

$ii)$ $y=816.3÷37.42\log y=\log 816.3-\log 37.42\log y=1.3387y=anti\log 1.3387y=21.812$

$iii)$ $y=0.000645\times 82.3\log y=\log 0.000645+\log 82.3\log y=-3.19+1.9154\log y=-1.275y=anti\log -1.275y=0.0531$

$iv)$ $y=0.3421÷0.09782\log y=\log 0.3421-\log 0.09782\log y=-0.4658+1.0095\log y=0.5437y=anti\log 0.5437y=3.4972$

$v)$ $y=(50.49{)}^5\log y=5\log 50.49=8.51603y=anti\log 8.51603y=328117957$

$vi)$ $y=\sqrt[3]{3561.4}\log y=\frac{1}{3}\log 561.4=\frac{1}{3}[\log 5.614+2\log 10]\log y=0.91642y=8.2494$

$vii)$ $y=\frac{175.23\times 22.159}{1828.56}\log y=\log 175.23+\log 22.159-\log 1828.56\log y=\log 1.7523+\log 2.2159-\log 1.82856+2\log 10+\log 10-3\log 10\log y=0.24361+0.3456-0.2621\log y=0.327y=2.123$

$viii)$ $y=\frac{\sqrt[3]{328}\times \sqrt[5]{5729}}{\sqrt{46.35}}\log y=\frac{1}{3}\log 28+\frac{1}{5}\log 729-\frac{1}{2}\log 46.35\log y=0.4824+0.5725-0.833\log y=0.222y=1.667$

$ix)$ $y=\frac{(76.25{)}^3\times \sqrt[3]{31.928}}{(42.75{)}^5\times 0.04623}\log y=3\log 76.25+\frac{1}{3}\log 1.928-5\log 42.75-\log 0.04623\log y=5.647+0.095-8.155-(-1.335)\log y=-1.078y=0.084$

$x)$ $y=\sqrt[3]{3\frac{0.7214\times 20.37}{69.8}}\log y=\frac{1}{3}[\log 0.7214+\log 20.37-\log 69.8]\log y=\frac{1}{3}[-0.142+1.309-1.844]\log y=-0.226y=0.5943$

$xi)$ $y={\log }_{9}63.28y=\frac{\log 63.28}{\log 9}=1.887$

$xii)$ $y={\log }_{3}7y=\frac{\log 7}{\log 3}=1.77$