Section 4.3: Logarithmic Functions

1. Relate the logarithmic function with base \(a\) to the exponential function with base \(a\).
2. Explain why the logarithm \(\log_{a} x\) of a number \(x\) is an exponent.
3. Specify the domain and range of a logarithmic function.
4. Evaluate logarithms \(\log_{a}x\) for a given value \(x\).
5. Sketch the graph of a logarithmic function \(f(x) = \log_{a} x\).
6. State the base of the common logarithm.
7. State the base of the natural logarithm.

Section 4.4: Laws of Logarithms

1. State the 3 “Laws of Logarithms” in the blue box on page 354 of Stewart, Redlin, and Watson.
2. Use the 3 “Laws of Logarithms” to expand and combine logarithmic expressions.
3. State common errors made when attempting to simplify logarithmic expressions, and identify them in a given attempted simplification.
4. State the change of base formula for converting from a logarithm base-\(b\) to a logarithm base-\(a\).
5. Use the change of base formula to convert from a logarithm base-\(a\) to a logarithm base-\(10\) or base-\(e\).

A Favorite Quote of Mine About Logarithms

Logarithmes are Numbers invented for the more easie working of questions in Arithmetike and Geometrie. The name is derived of Logos, which signifies Reason, and Arithmos, signifying Numbers. By them all troublesome Multiplications and Divisions in Arithmetike are avoided, and performed onely by Addition in stead of Multiplication, and by Subtraction in stead of Division.

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There is nothing (right well beloved Students in the Mathematickes) that is so troublesome to Mathematicall practice, not that doth more molest and hinder Calculators, then the Multiplications, Divisions, square and cubical Extractions of great numbers, which besides the tedious expence of time, are for the most part subject to many slippery errors.