91Ó°ÊÓ

Rewrite each equation in logarithmic form. $$ 5^{y}=x $$

Simplify using logarithm properties to a single logarithm. $$ \ln \left(4 x^{2}\right)+\ln \left(3 x^{3}\right) $$

The amount of area covered by blackberry bushes in a park has been growing by \(12 \%\) each year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate area that will be covered in 2020 .

Sketch a graph of each pair of function $$ f(x)=\log _{2}(x), g(x)=\log _{4}(x) $$

Use regression to find an exponential equation that best fits the data given. $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \mathbf{y} & 643 & 829 & 920 & 1073 & 1330 & 1631 \\ \hline \end{array} $$

Simplify using logarithm properties to a single logarithm. $$ \ln \left(6 x^{9}\right)-\ln \left(3 x^{2}\right) $$

A vehicle purchased for \(\$ 32,500\) depreciates at a constant rate of \(5 \%\) each year. Determine the approximate value of the vehicle 12 years after purchase.

Rewrite each equation in logarithmic form. $$ c^{d}=k $$

Use regression to find an exponential equation that best fits the data given. $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \mathbf{y} & 555 & 383 & 307 & 210 & 158 & 122 \\ \hline \end{array} $$

A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of the population after: a) 2 hours, b) 100 minutes