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Chapter 4: Problem 38
Evaluate each expression without using a calculator. $$\log _{6} 1$$
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Find the domain of each logarithmic function. $$f(x)=\ln \left(x^{2}-x-2\right)$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because the equations $$\log (3 x+1)=5 \text { and } \log (3 x+1)=\log 5$$ are similar, I solved them using the same method.
Use the formula \(t=\frac{\ln 2}{k}\) that gives the time for a population with a growth rate \(k\) to double to solve Exercises \(35-36 .\) Express each answer to the nearest whole year. The growth model \(A=112.5 e^{0.012 y}\) describes Mexico's population, \(A,\) in millions, \(t\) years after 2010 . a. What is Mexico's growth rate? b. How long will it take Mexico to double its population?
In Exercises \(53-56,\) rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$ y=2.5(0.7)^{x} $$
Without using a calculator, determine which is the greater number: \(\log _{4} 60\) or \(\log _{3} 40\).
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