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Chapter 3: Problem 20
Write the exponential equation in logarithmic form. For example, the logarithmic form of \(2^{3}=8\) is \(\log _{2} 8=3\). $$4^{-3}=\frac{1}{64}$$
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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. Find the \(\mathrm{pH}\) if \(\left[\mathrm{H}^{+}\right]=2.3 \times 10^{-5}\).
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 4 x-\log (12+\sqrt{x})=2$$
Use the Richter scale \(R=\log \frac{l}{I_{0}}\) for measuring the magnitudes of earthquakes. Find the magnitude \(R\) of each earthquake of intensity \(I\) (let \(I_{0}=1\) ). (a) \(I=199,500,000\) (b) \(I=48,275,000\) (c) \(I=17,000\)
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log (3 x+4)=\log (x-10)$$
The demand equation for a limited edition coin set is \(p=1000\left(1-\frac{5}{5+e^{-0.001 x}}\right)\) Find the demand \(x\) for a price of (a) \(p=\$ 139.50\) and (b) \(p=\$ 99.99\).
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