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Chapter 3: Problem 5
Match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\ln u^{n}=n \ln u$$
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Write two or three sentences stating the general guidelines that you follow when solving (a) exponential equations and (b) logarithmic equations.
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. Compute \(\left[\mathrm{H}^{+}\right]\) for a solution in which \(\mathrm{pH}=3.2\).
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?
$$\$ 2500$$ is invested in an account at interest rate \(r\), compounded continuously. Find the time required for the amount to (a) double and (b) triple. $$r=0.025$$
After discontinuing all advertising for a tool kit in \(2004,\) the manufacturer noted that sales began to drop according to the model \(S=\frac{500,000}{1+0.4 e^{k t}}\) where \(S\) represents the number of units sold and \(t=4\) represents \(2004 .\) In \(2008,\) the company sold 300,000 units. (a) Complete the model by solving for \(k\). (b) Estimate sales in 2012 .
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