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Chapter 4: Problem 69
Evaluate each expression without using a calculator. $$\ln e^{6}$$
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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. $$ \log _{9}\left(\frac{9}{x}\right) $$
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. $$ \frac{1}{2}\left(\log _{5} x+\log _{5} y\right)-2 \log _{5}(x+1) $$
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. $$ 2 \log _{b} x+3 \log _{b} y $$
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 \(41-70\), 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. $$ 2 \ln x-\frac{1}{2} \ln y $$
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