91Ó°ÊÓ

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \frac{\log _{5} 25+2 \log _{10} 10}{\log _{16} 4} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log \sqrt{a} $$

The formula \(t=\frac{\log K}{0.045 \log e}\) gives the time \(t\) (in years) that it will take an investment \(P\) that is compounded continuously at a rate of 4.5\(\%\) to increase to an amount \(K\) times the original principal. a. Use the formula to complete the table to three decimal places. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline K & {1} & {2} & {3} & {4} & {5} & {10} & {20} & {30} \\ \hline t & {} & {} & {} & {} & {} & {} \\ \hline\end{array} $$ b. Use the table to graph the function \(t=\frac{\log K}{0.045 \log e}\) c. If Paul invests \(\$ 1,000\) in a savings account that is compounded continuously at a rate of \(4.5 \%,\) when will his investment double? triple?

In \(57-68,\) solve each equation for the variable. $$ \log _{8} x=\frac{1}{2} $$