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Problem 1
Evaluate the expressions in Exercises \(1-16\). $$ 3^{3} $$
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Let \(a=\log 2, b=\log 3,\) and \(c=\log 7.\) Use the logarithm identities to express the given quantity in terms of \(a, b,\) and \(c .\) $$ \log \left(\frac{4}{7}\right) $$
Let \(a=\log 2, b=\log 3,\) and \(c=\log 7.\) Use the logarithm identities to express the given quantity in terms of \(a, b,\) and \(c .\) $$ \log \left(\frac{2}{9}\right) $$
Convert the expressions to power form. $$ \sqrt{3} $$
Complete the given tables. $$ \begin{array}{|r|l|l|l|l|} \hline \begin{array}{r} \text { Exponential } \\ \text { Form } \end{array} & & & & & \\ \hline \begin{array}{r} \text { Logarithmic } \\ \text { Form } \end{array} & \log _{0.3} 0.09=2 & \log _{1 / 2} 1=0 & \log _{10} 0.001=-3 & \log _{9} \frac{1}{81}=-2 & \log _{2} 1,024=10 & \log _{64} \frac{1}{4}=-\frac{1}{3} \\ \hline \end{array} $$
Solve the given equation for the indicated variable. $$ 27=3^{2 x-1} $$
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