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Chapter 4: Problem 17
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. $$ \log N^{-6} $$
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If \(f(x)=\log _{\phi} x,\) show that \(\frac{f(x+h)-f(x)}{h}=\log _{b}\left(1+\frac{h}{x}\right)^{1 / h}, h \neq 0\)
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. $$ \ln \left(\frac{e^{2}}{5}\right) $$
Rescarch applications of logarithmic functions as mathematical models and plan a seminar based on your group's research. Each group member should research one of the following areas or any other area of interest: \(\mathrm{pH}\) (acidity of solutions), intensity of sound (decibels), brightness of stars, consumption of natural resources, human memory, progress over time in a sport, profit over time. For the area that you select. explain how logarithmic functions are used and provide examples.
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. $$ \log _{3} 405-\log _{3} 5 $$
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