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Chapter 12: Problem 15
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b} x^{3}$$
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Describe the change-of-base property and give an example.
Without showing the details, explain how to condense \(\ln x-2 \ln (x+1)\)
Complete the table for a savings account subject to n compounding periods per year \(\left[A=P\left(1+\frac{r}{n}\right)^{n t}\right]\) Round answers to one decimal place. $$\begin{array}{l|c|l|l|l} \hline \begin{array}{l} \text { Amount } \\ \text { Invested } \end{array} & \begin{array}{l} \text { Number of } \\ \text { Compounding } \\ \text { Periods } \end{array} & \begin{array}{l} \text { Annual Interest } \\ \text { Rate } \end{array} & \begin{array}{l} \text { Accumulated } \\ \text { Amount } \end{array} & \begin{array}{l} \text { Time } t \\ \text { in Years } \end{array} \\ \hline \$ 1000 & 360 & & \$ 1400 & 2 \\ \hline \end{array}$$
The function \(P(t)=145 e^{-0.092 t}\) models a runner's pulse, \(P(t),\) in beats per minute, \(t\) minutes after a race, where \(0 \leq t \leq 15 .\) Graph the function using a graphing utility. [TRACE] along the graph and determine after how many minutes the runner's pulse will be 70 beats per minute. Round to the nearest tenth of a minute. Verify your observation algebraically.
Solve each equation. $$5^{x^{2}-12}=25^{2 x}$$
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