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Chapter 4: Problem 28
Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{9}$$
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Describe the product rule for logarithms and give an example.
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. $$ \log _{b}\left(\frac{V x y^{3}}{z^{3}}\right) $$
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. $$ \frac{1}{3}\left|2 \ln (x+5)-\ln x-\ln \left(x^{2}-4\right)\right| $$
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. $$ 5 \ln x-2 \ln y $$
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. $$ \log \left[\frac{100 x^{3} \sqrt[3]{5-x}}{3(x+7)^{2}}\right] $$
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