3-3 Study Guide and Intervention

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P. Study Guide and Intervention. Common Logarithms. Study Guide and Intervention (continued) kalian sem Common Logarithms. Change of Base Formula The following

Study Guide and Intervention

6 11. 10. 12 6 3 2(4) 6. 11. 14 (8 20 2). 7. 12. 6(7) 4 4 5 38. 13. 8(42 Study Guide and Intervention (continued) ... Sample answers are given.

7-5 - Study Guide and Intervention

Lesson 7-5. NAME. DATE. PERIOD. PDF Pass. Chapter 7. 33. Glencoe Algebra 2. Properties of Logarithms Properties of exponents can be used to develop the.

Chapter 10 Resource Masters

Study Guide and Intervention Workbook. 0-07-828029-X 1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02 ... common logarithm. LAW·guh·RIH·thuhm.

7-6 Study Guide and Intervention

Answer Key. 7-6 Study Guide and Intervention. Growth and Decay. NAME. Exponential Growth. Exponential Growth Population increases and growth of monetary

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9-2 Study Guide and Intervention (continued). Logarithms and Logarithmic Functions. Solve Logarithmic Equations and Inequalities. If b > 1 x > 0

Chapter 10: Exponential and Logarithmic Relations

Solve exponential equations and inequalities using common logarithms. Study Guide and Intervention CRM pp. 573–574

3-3 Study Guide and Intervention - Properties of Logarithms

Therefore you will often use this formula

Study Guide and Intervention

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.

10-1 Study Guide and Intervention

6. Glencoe Precalculus. 10-1 Study Guide and Intervention(continued). Sequences Series

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 3 15 Glencoe Precalculus

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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[PDF] 3-3 Study Guide and Intervention - Properties of Logarithms

Chapter 3 15 Glencoe Precalculus

3-3 Study Guide and Intervention

Properties of Logarithms

Example 2: Expand ln ૡ࢞૞

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

Chapter 3 16 Glencoe Precalculus

3-3 Study Guide and Intervention (continued)

Properties of Logarithms

Formula is required.

Example: Evaluate each logarithm.

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