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Chapter 4: Problem 36
Evaluate each expression without using a calculator. $$\log _{4} 4^{6}$$
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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 \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \log x+\log 15+\log \left(x^{2}-4\right)-\log (x+2) $$
In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \ln x+\ln 7 $$
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. $$ \log \left[\frac{100 x^{3} \sqrt[3]{5-x}}{3(x+7)^{2}}\right] $$
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. $$ \log _{9}(9 x) $$
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