91Ó°ÊÓ

Express as a difference of logarithms. $$\log _{b} \frac{3}{w}$$

Newton's Law of Cooling. Suppose that a body with temperature \(T_{1}\) is placed in surroundings with temperature \(T_{0}\) different from that of \(T_{1}\). The body will either cool or warm to temperature \(T(t)\) after time \(t,\) in minutes, where $$T(t)=T_{0}+\left(T_{1}-T_{0}\right) e^{-i t}$$When Was the Murder Committed? The police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12: 00 P.M. She immediately takes the temperature of the body and finds it to be \(94.6^{\circ} \mathrm{F}\). She then takes the temperature 1 hr later and finds it to be \(93.4^{\circ} \mathrm{F}\). The temperature of the room is \(70^{\circ} \mathrm{F}\). When was the murder committed?

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$5^{x+2}=4^{1-x}$$

Graph the function by substituting and plotting points. Then check your work using a graphing calculator. $$y=\frac{1}{4} e^{x}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$(3.9)^{x}=48$$

Express in terms of sums and differences of logarithms. $$\log _{a} 6 x y^{5} z^{4}$$

Find each of the following. Do not use a calculator. $$\log _{3} \sqrt[4]{3}$$

Express in terms of sums and differences of logarithms. $$\log _{a} x^{3} y^{2} z$$

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$250-(1.87)^{x}=0$$

Find each of the following. Do not use a calculator. $$\log 10^{8 / 5}$$