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Chapter 3: Problem 9
Write the logarithmic equation in exponential form. For example, the exponential form of \(\log _{5} 25=2\) is \(5^{2}=25\). $$\log _{9} \frac{1}{81}=-2$$
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Determine the time necessary for $$\$ 1000$$to double if it is invested at interest rate \(r\) compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. $$r=6.5 \%$$
Determine whether the statement is true or false. Justify your answer. The domain of a logistic growth function cannot be the set of real numbers.
Use the acidity model given by \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right],\) where acidity \((\mathrm{pH})\) is a measure of the hydrogen ion concentration \(\left[\mathrm{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. The \(\mathrm{pH}\) of a solution is decreased by one unit. The hydrogen ion concentration is increased by what factor?
Use the acidity model given by \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right],\) where acidity \((\mathrm{pH})\) is a measure of the hydrogen ion concentration \(\left[\mathrm{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. Apple juice has a pH of 2.9 and drinking water has a pH of \(8.0 .\) The hydrogen ion concentration of the apple juice is how many times the concentration of drinking water?
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{3} x+\log _{3}(x-8)=2$$
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