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Chapter 12: Problem 31
Evaluate each expression without using a calculator. $$\log _{2} \frac{1}{\sqrt{2}}$$
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Graph each of the following functions in the same viewing rectangle and then place the functions in order from the one that increases most slowly to the one that increases most rapidly. $$y=x, y=\sqrt{x}, y=e^{x}, y=\ln x, y=x^{x}, y=x^{2}$$
Describe the relationship between an equation in logarithmic form and an equivalent equation in exponential form.
Solve each equation. $$5^{2 x} \cdot 5^{4 x}=125$$
In many states, a \(17 \%\) risk of a car accident with a blood alcohol concentration of 0.08 is the lowest level for charging a motorist with driving under the influence. Do you agree with the \(17 \%\) risk as a cutoff percentage, or do you feel that the percentage should be lower or higher? Explain your answer. What blood alcohol concentration corresponds to what you believe is an appropriate percentage?
Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$\log (x+3)+\log x=1$$
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