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Chapter 3: Problem 49
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$3 \ln 5 x=10$$
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Writing Use your school's library, the Internet, or some other reference source to write a paper describing John Napier's work with logarithms.
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.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$4 \log (x-6)=11$$
The graph of \(f(x)=\log _{3} x\) contains the point \((27,3)\)
Monthly Payment The model \(t=16.625 \ln \left(\frac{x}{x-750}\right), \quad x>750\) approximates the length of a home mortgage of \(\$ 150,000\) at \(6 \%\) in terms of the monthly payment. In the model, \(t\) is the length of the mortgage in years and \(x\) is the monthly payment in dollars. (a) Use the model to approximate the lengths of a \(\$ 150,000\) mortgage at \(6 \%\) when the monthly payment is \(\$ 897.72\) and when the monthly payment is \(\$ 1659.24\)(c) Approximate the total interest charges for a monthly payment of \(\$ 897.72\) and for a monthly payment of \(\$ 1659.24\) (d) What is the vertical asymptote for the model? Interpret its meaning in the context of the problem.
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