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x is usually written without the subscript as log x Use the LOG key on your calculator to evaluate common logarithms The relation between exponents and 

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9-4 Study Guide and Intervention Common Common La hms Base 10 logarithms are called common logarithms The your calculator to evaluate common logarithms 28 Glencoe Algebra 2 Chapter 9 29 Glencoe Algebra 2 NA Answers

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Therefore, you will often use this formula, especially for scientific applications Either of the following forms will provide the correct answer log x = log log 

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Logarithmic Functions and Expressions Definition of The inverse of the exponential function y = bx is the logarithmic function x = by 7-3 Study Guide and Intervention Properties of the parent function are described in the following table

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Common Logarithms Base 10 logarithms are called common logarithms The expression log 10 x is usually written without the subscript as log x Use the LOG

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Guide and Intervention Properties of Real Numbers Properties of Equality You can solve equations by using addition, subtraction, Always check your answers by substituting them into the original equation 2-3 Study Guide and Intervention (continued) Definition of Logarithm Let b and x be positive numbers, b 1

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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 3 15 Glencoe Precalculus

3-3 Study Guide and Intervention

Properties of Logarithms

Properties of Logarithms Since logarithms and exponents have an inverse relationship, they have certain properties

that can be used to make them easier to simplify and solve.

If b, x, and y are positive real numbers, b p is a real number, then the following statements are true.

௕ xy = ௕ x + ௕ y Product Property ௬ = ௕ x ௕ y Quotient Property ௕ݔ௣ = p ௕ x Power Property = 3(3)(1) + 5(1)(1) ௫ x = 1 = 4 Simplify.

Example 2: Expand ln ૡ࢞૞

ln ଼௫ఱ = ln 8 + 5 ln x ln 3 2 ln y Power Property

Exercises

1. Evaluate 2 ଷ 27 + 4 ଷ ଵ

Expand each expression.

2. ଷ ହ௥ఱ

Condense each expression.

4. 11 ଽ (x 3) 5 ଽ 2x 5. ଷ

ସ ln (2h k) + ଷ ହ ln (2h + k) log3 5 + 5 log3 r ૛ ૜ log3 t log (a 2) + 6 log (b + 4) log 9 5 log (b 2) log9

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 3 16 Glencoe Precalculus

3-3 Study Guide and Intervention (continued)

Properties of Logarithms

Change of Base Formula If the logarithm is in a base that needs to be changed to a different base, the Change of Base

Formula is required.

For any positive real numbers a, b, and x, a b ୠ x = ୪୭୥ೌ௫

Many non-graphing calculators cannot be used for logarithms that are not base e or base 10. Therefore, you will often use

this formula, especially for scientific applications. Either of the following forms will provide the correct answer.

௕ x = ୪୭୥௫ ୪୭୥௕ ௕ x = ୪୬௫

Example: Evaluate each logarithm.

૜ 10 య10 = ୪୭୥ଵ଴ య Change of Base Formula

Use a calculator. 2.10 Use a calculator.

Exercises

Evaluate each logarithm.

4. ଺ 94 5. ହ 256 6. ଽ 712

7. ଺ 832 8. ଵଵ 47 9. ଷ 9

1.86 2.58 3.60

2.54 3.45 2.99

3.753 1.606 2

2.667 3.367 8.714

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