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Chapter 3: Problem 87
Use the One-to-One Property to solve the equation for \(x\). $$\log (2 x+1)=\log 15$$
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The demand equation for a hand-held electronic organizer is \(p=5000\left(1-\frac{4}{4+e^{-0.002 x}}\right)\) Find the demand \(x\) for a price of (a) \(p=\$ 600\) and (b) \(p=\$ 400\).
The number of bacteria in a culture is increasing according to the law of exponential growth. After 3 hours, there are 100 bacteria, and after 5 hours, there are 400 bacteria. How many bacteria will there be after 6 hours?
Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$2 x^{2} e^{2 x}+2 x e^{2 x}=0$$
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?
Use your school's library, the Internet, or some other reference source to write a paper describing John Napier's work with logarithms.
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