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Chapter 4: Problem 62
Evaluate each expression without using a calculator. $$\log 1000$$
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In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{b}\left(\frac{x^{3} y}{z^{2}}\right) $$
In Exercises \(71-78,\) use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$ \log _{0.1} 17 $$
Which one of the following is true? a. \(\frac{\log _{7} 49}{\log _{7} 7}=\log _{7} 49-\log _{7} 7\) b. \(\log _{b}\left(x^{3}+y^{3}\right)=3 \log _{b} x+3 \log _{b} y\) c. \(\log _{b}(x y)^{5}=\left(\log _{b} x+\log _{b} y\right)^{5}\) d. \(\ln \sqrt{2}=\frac{\ln 2}{2}\)
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{5} \sqrt[3]{\frac{x^{2} y}{25}} $$
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{7}(7 x) $$
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