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Chapter 12: Problem 1
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{5}(7 \cdot 3)$$
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Without showing the details, explain how to condense \(\ln x-2 \ln (x+1)\)
Because the equations $$\log (3 x+1)=5 \text { and } \log (3 x+1)=\log 5$$ are similar, I solved them using the same method.
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?
Factor completely: $$6 x^{2}-8 x y+2 y^{2}$$ (Section 6.5, Example 8)
Solve each equation. $$5^{2 x} \cdot 5^{4 x}=125$$
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