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Chapter 13: Problem 28
Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{3} 27 m$$
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Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true. The domain of \(f\) is the range of \(f^{-1}\)
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 \(1 .\) $$4 \log _{3} t-2 \log _{3} 6-2 \log _{3} u$$
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 \(1 .\) $$\log _{7} d-\log _{7} 3$$
Show that the inverse of \(y=\ln x\) is \(y=e^{x}\).
The number of bacteria, \(N(t),\) in a culture \(t\) hr after the bacteria is placed in a dish is given by $$N(t)=4000 e^{0.0374 t}$$ where 4000 bacteria are initially present. a) After how many hours will there be 5000 bacteria in the culture? b) How long will it take for the number of bacteria to double?
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