91Ó°ÊÓ

For the following exercises, rewrite each equation in exponential form. $$\log _{y}(x)=-11$$

For the following exercises, evaluate the base \(b\) logarithmic expression without using a calculator. $$\log _{3}\left(\frac{1}{27}\right)$$

What type(s) of translation(s), if any, affect the range of a logarithmic function?

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ 4 \log _{7}(c)+\frac{\log _{7}(a)}{3}+\frac{\log _{7}(b)}{3} $$

For the following exercises, suppose log \(_{5}(6)=a\) and \(\log _{5}(11)=b\) . Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of \(a\) and \(b .\) Show the steps for solving. $$ \log _{6}(55) $$

Use logarithms to solve. \(e^{r+10}-10=-42\)

Solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate \(x\) to 3 decimal places. \(1000(1.03)^{t}=5000\) using the common log.

Define Newton's Law of Cooling. Then name at least three real-world situations where Newton's Law of Cooling would be applied.

For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of \(100^{\circ}\) Falrenheit was taken off the stove to cool in a \(69^{\circ} \mathrm{F}\) room. After fifteen minutes, the internal temperature of the soup was \(95^{\circ} \mathrm{F}\) . Use Newton’s Law of Cooling to write a formula that models this situation.

For the following exercises, use this scenario The equation \(N(t)=\frac{500}{1+49 e^{-0.7 t}}\) models the number of people in a town who have heard a rumor after \(t\) days. To the nearest whole number, how many people will have heard the rumor after 3 days?