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Chapter 3: Problem 21
Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{x}-9=19$$
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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.
Function \(\quad\) Value \(\begin{array}{ll}\text { 57. } f(x)=\ln x & x=18.42 \\ \text { 58. } f(x)=3 \ln x & x=0.74\end{array}\) \(\begin{array}{lll}y & f(x)=3 \ln x & x=0.74 \\ \text { 59. } g(x)=8 \ln x & x=0.05\end{array}\) 60\. \(g(x)=-\ln x \quad x=\frac{1}{2}\)
Let \(f(x)=\log _{a} x\) and \(g(x)=a^{x},\) where \(a>1\) (a) Let \(a=1.2\) and use a graphing utility to graph the two functions in the same viewing window. What do you observe? Approximate any points of intersection of the two graphs. (b) Determine the value(s) of \(a\) for which the two graphs have one point of intersection. (c) Determine the value(s) of \(a\) for which the two graphs have two points of intersection.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 8 x-\log (1+\sqrt{x})=2$$
You invest \(\$ 2500\) in an account at interest rate \(r,\) compounded continuously. Find the time required for the amount to (a) double and (b) triple. $$r=0.025$$
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