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Chapter 4: Problem 108
Without showing the details, explain how to condense \(\ln x-2 \ln (x+1)\)
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The exponential growth models describe the population of the indicated country, \(A,\) in millions, t years after 2006 . $$ \begin{array}{ll} {\text { Canada }} & {A=33.1 e^{0.009 t}} \\ {\text { Uganda }} & {A=28.2 e^{0.034 t}} \end{array} $$ Use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The models indicate that in 2013 , Uganda's population will exceed Canada's.
Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$ 3^{x+1}=9 $$
Check each proposed solution by direct substitution or with a graphing utility. $$ (\log x)(2 \log x+1)=6 $$
Given \(f(x)=\frac{2}{x+1}\) and \(g(x)=\frac{1}{x},\) find each of the following: a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) (Section \(2.6, \text { Example } 6)\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can solve \(4^{x}=15\) by writing the equation in logarithmic form.
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