a.	$\begin{align}&\frac{{8.765}\times^3\sqrt{27.03}}{24.51}\\[5pt] \lg &=lg(\frac{{8.765}\times^3\sqrt{27.03}}{24.51})\\[5pt] &=lg{8.765}+{\frac{1}{3}lg27.03} -lg24.51\\[5pt] &={0.9427}+{\frac{1}{3}\times 1.4319} -1.3894\\[5pt] &={0.9427}+{0.4773} -1.3894\\[5pt] &={0.0306}\\[5pt] &=antilog 0.0306\\[5pt] &=\underline{ \underline {1.073}} \end{align}$
b.	$\begin{align}&\frac{{\sqrt{9.18}}\times{8.02^2}}{9.83}\\[5pt] lg&=lg(\frac{{\sqrt{9.18}}\times{8.02^2}}{9.83})\\[5pt] &=lg{\sqrt{9.18}}+lg{8.02^2}-lg{9.83}\\[5pt] &={\frac{1}{2}\times 0.9628} +2\times{0.9042} -0.9926\\[5pt] &={0.4814}+{1.8084} -0.9926\\[5pt] &={1.2972}\\[5pt] &=antilog 1.2972\\[5pt] &=\underline{ \underline {19.82}} \end{align}$
c.	$\begin{align}&\frac{{\sqrt{0.0945}}\times{4.821^2}}{48.15}\\[5pt] lg&=lg(\frac{{\sqrt{0.0945}}\times{4.821^2}}{48.15})\\[5pt] &=\lg{\sqrt{0.0945}}+lg{4.821^2}-lg{48.15}\\[5pt] &={\frac{1}{2}\times \bar{2}.9754} +2\times{0.6831} -1.6825\\[5pt] &=\bar{1}{.4877}+{1.3662} -1.6825\\[5pt] &=-1+0.4877+1+0.3662 -1-0.6825\\[5pt] &=-1+0.4877+0.3662 -0.6825\\[5pt] &=-1+0.1714\\[5pt] &=\bar{1}{.1714}\\[5pt] &=antilog \bar{1}{.1714}\\[5pt] &=\underline{ \underline {0.1483}} \end{align}$
d.	$\begin{align}&\frac{{3}\times{0.752^2}}{\sqrt{17.96}}\\[5pt] lg&=(\frac{{3}\times{0.752^2}}{\sqrt{17.96}})\\[5pt] &=lg{3}+lg{0.752^2}-lg{\sqrt{17.96}}\\[5pt] &= {0.4771}+2\times \bar{1}.{8762}-{\frac{1}{2}\times{1.2544}}\\[5pt] &=0.4771+\bar{1}{.7524} -0.6272\\[5pt] &=0.2295-0.6272\\[5pt] &=-0.3977\\[5pt] &=-1+1-0.3977\\[5pt] &=-1+0.6023\\[5pt] &=\bar{1}{.6023}\\[5pt] &=antilog \bar{1}{.6023}\\[5pt] &=\underline{ \underline {0.4002}} \end{align}$
e.	$\begin{align}&\frac{{6.591}\times{^3\sqrt{0.0782}}}{0.9821^2}\\[5pt] lg&=(\frac{{6.591}\times{^3\sqrt{0.0782}}}{0.9821^2})\\[5pt] &=\lg{6.591}+lg{^3\sqrt{0.0782}}-lg{0.9821^2}\\[5pt] &=0.8190+{\frac{1}{3}\times \bar{2}.8932}-2\times\bar{1}{.9921}\\[5pt] &={0.8190}+\bar{1}.{6310}-\bar{1}.{9842}\\[5pt] &=0.4658\\[5pt] &=antilog 0.4658\\[5pt] &=\underline{ \underline {2.923}} \end{align}$
f.	$\begin{align}&\frac{{3.251}\times{^3\sqrt{0.0234}}}{0.8915}\\[5pt] lg&=(\frac{{3.251}\times{^3\sqrt{0.0234}}}{0.8915})\\[5pt] &=\lg{3.251}+lg{^3\sqrt{0.0234}}-lg{0.8915}\\[5pt] &=0.5120+{\frac{1}{3}\times \bar{2}.3692}-\bar{1}{.9501}\\[5pt] &={0.5120}+\bar{1}.{4564}-\bar{1}.{9501}\\[5pt] &=0.5120-1+0.4564-(-1+0.9501)\\[5pt] &=0.5120-1+0.4564+1-0.9501\\[5pt] &=0.5120+0.4564-0.9501\\[5pt] &=0.0183\\[5pt] &=antilog 0.0183\\[5pt] &=\underline{ \underline {1.043}} \end{align}$

By studying this lesson you will be able to

Use the table of logarithms to simplify expressions involving products and quotients of powers and roots of numbers 0 and1.