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Chapter 13: Problem 1
What is the base of \(\ln x ?\)
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If \(f(x)=-6 x+4,\) show that \(f^{-1}(x)=-\frac{1}{6} x+\frac{2}{3}\)
Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$2 \log _{9} m-4 \log _{9} 2-4 \log _{9} n$$
Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$\log \left(r^{2}+3\right)-2 \log \left(r^{2}-3\right)$$
The number of bacteria, \(N(t),\) in a culture \(t\) hr after the bacteria is placed in a dish is given by $$N(t)=10,000 e^{0.0418 t}$$ where \(10,000\) bacteria are initially present. a) After how many hours will there be \(15,000\) bacteria in the culture? b) How long will it take for the number of bacteria to double?
Determine whether each function is one-to-one. If it is one-to-one, find its inverse. $$g=\\{(2,1),(5,2),(7,14),(10,19)\\}$$
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