Learning Materials
Features
Discover
Chapter 3: Problem 98
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$4 \log (x-6)=11$$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
You are investing \(P\) dollars at an annual interest rate of \(r,\) compounded continuously, for \(t\) years. Which of the following would result in the highest value of the investment? Explain your reasoning. (a) Double the amount you invest. (b) Double your interest rate. (c) Double the number of years.
A $$\$ 120,000$$ home mortgage for 30 years at \(7 \frac{1}{2} \%\) has a monthly payment of $$\$ 839.06 .$$ Part of the monthly payment is paid toward the interest charge on the unpaid balance, and the remainder of the payment is used to reduce the principal. The amount that is paid toward the interest is \(u=M-\left(M-\frac{P r}{12}\right)\left(1+\frac{r}{12}\right)^{12 t}\) and the amount that is paid toward the reduction of the principal is \(v=\left(M-\frac{P r}{12}\right)\left(1+\frac{r}{12}\right)^{12 t}\) In these formulas, \(P\) is the size of the mortgage, \(r\) is the interest rate, \(M\) is the monthly payment, and \(t\) is the time (in years). (a) Use a graphing utility to graph each function in the same viewing window. (The viewing window should show all 30 years of mortgage payments.) (b) In the early years of the mortgage, is the larger part of the monthly payment paid toward the interest or the principal? Approximate the time when the monthly payment is evenly divided between interest and principal reduction. (c) Repeat parts (a) and (b) for a repayment period of 20 years \((M=\$ 966.71) .\) What can you conclude?
The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y=0.7979 e^{-(x-5.4)^{2} / 0.5},\) \(4 \leq x \leq 7,\) where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.
Use the acidity model given by \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right],\) where acidity \((\mathrm{pH})\) is a measure of the hydrogen ion concentration \(\left[\mathrm{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. The \(\mathrm{pH}\) of a solution is decreased by one unit. The hydrogen ion concentration is increased by what factor?
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2}(2 x-3)=\log _{2}(x+4)$$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine