Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 10.4, Problem 32WE

a.

To determine

Simplify the logarithmic expressions log28 and log82 .

a.

Expert Solution
Check Mark

Answer to Problem 32WE

  log28=3 and log82=13 .

Explanation of Solution

Given information: The given expression is,

  log28 and log82 ....(1)

Calculation: Simplify (1),

  log28=log2(2)3=3log22 ....(logamn=nlogam) =3(1) ....(∵logaa=1)=3

Similarly,

  log82=loge(2)loge(8)=loge(2)loge(2)3=loge(2)3loge(2)=13

Hence log28=3 and log82=13 .

b.

To determine

Simplify the logarithmic expressions log33 and log33 .

b.

Expert Solution
Check Mark

Answer to Problem 32WE

  log33=12 and log33=2 .

Explanation of Solution

Given information: The given expression is,

  log33 and log33 (2)

Calculation: Simplify (2),

  log33=log3(3)12=12log33 ....(logamn=nlogam) =12(1) ....(∵logaa=1)=12

Similarly,

  log33=loge(3)loge(3)=loge(3)loge(3)12=loge(3)(1/2)loge(3)=2

Hence log33=12 and log33=2 .

c.

To determine

State the generalization based on parts (a) and (b).

c.

Expert Solution
Check Mark

Answer to Problem 32WE

The generalizations based on parts (a) and (b) are logb(a)=loge(a)loge(b) and logb(a)×loga(b)=1 .

Explanation of Solution

Given information: The given expressions to simplify are written in (1) and (2).

Calculation: From the simplified values of (1) and (2) the generalization based on parts (a) and (b) are,

  logb(a)=loge(a)loge(b) and logb(a)×loga(b)=1

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Chapter 10.4, Problem 31WE
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Chapter 10.4, Problem 33WE

Chapter 10 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
Ch. 10.1 - Prob. 11OECh. 10.1 - Prob. 12OECh. 10.1 - Prob. 13OECh. 10.1 - Prob. 14OECh. 10.1 - Prob. 15OECh. 10.1 - Prob. 16OECh. 10.1 - Prob. 17OECh. 10.1 - Prob. 18OECh. 10.1 - Prob. 19OECh. 10.1 - Prob. 20OECh. 10.1 - Prob. 21OECh. 10.1 - Prob. 22OECh. 10.1 - Prob. 23OECh. 10.1 - Prob. 24OECh. 10.1 - Prob. 25OECh. 10.1 - Prob. 26OECh. 10.1 - Prob. 27OECh. 10.1 - Prob. 28OECh. 10.1 - Prob. 29OECh. 10.1 - Prob. 30OECh. 10.1 - Prob. 31OECh. 10.1 - Prob. 1WECh. 10.1 - Prob. 2WECh. 10.1 - Prob. 3WECh. 10.1 - Prob. 4WECh. 10.1 - Prob. 5WECh. 10.1 - Prob. 6WECh. 10.1 - Prob. 7WECh. 10.1 - Prob. 8WECh. 10.1 - Prob. 9WECh. 10.1 - Prob. 10WECh. 10.1 - Prob. 11WECh. 10.1 - Prob. 12WECh. 10.1 - Prob. 13WECh. 10.1 - Prob. 14WECh. 10.1 - Prob. 15WECh. 10.1 - Prob. 16WECh. 10.1 - Prob. 17WECh. 10.1 - Prob. 18WECh. 10.1 - Prob. 19WECh. 10.1 - Prob. 20WECh. 10.1 - Prob. 21WECh. 10.1 - Prob. 22WECh. 10.1 - Prob. 23WECh. 10.1 - Prob. 24WECh. 10.1 - Prob. 25WECh. 10.1 - Prob. 26WECh. 10.1 - Prob. 27WECh. 10.1 - 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Prob. 27WECh. 10.5 - Prob. 28WECh. 10.5 - Prob. 29WECh. 10.5 - Prob. 30WECh. 10.5 - Prob. 31WECh. 10.5 - Prob. 32WECh. 10.5 - Prob. 33WECh. 10.5 - Prob. 34WECh. 10.5 - Prob. 35WECh. 10.5 - Prob. 36WECh. 10.5 - Prob. 37WECh. 10.5 - Prob. 38WECh. 10.5 - Prob. 39WECh. 10.5 - Prob. 40WECh. 10.5 - Prob. 41WECh. 10.5 - Prob. 42WECh. 10.5 - Prob. 43WECh. 10.5 - Prob. 44WECh. 10.5 - Prob. 45WECh. 10.5 - Prob. 46WECh. 10.5 - Prob. 47WECh. 10.5 - Prob. 48WECh. 10.5 - Prob. 49WECh. 10.5 - Prob. 50WECh. 10.5 - Prob. 51WECh. 10.5 - Prob. 1MRECh. 10.5 - Prob. 2MRECh. 10.5 - Prob. 3MRECh. 10.5 - Prob. 4MRECh. 10.5 - Prob. 5MRECh. 10.5 - Prob. 6MRECh. 10.5 - Prob. 7MRECh. 10.5 - Prob. 8MRECh. 10.5 - Prob. 9MRECh. 10.5 - Prob. 10MRECh. 10.5 - Prob. 11MRECh. 10.5 - Prob. 12MRECh. 10.5 - Prob. 13MRECh. 10.5 - Prob. 1STCh. 10.5 - Prob. 2STCh. 10.5 - Prob. 3STCh. 10.5 - Prob. 4STCh. 10.5 - Prob. 5STCh. 10.5 - Prob. 6STCh. 10.5 - Prob. 7STCh. 10.6 - Prob. 1OECh. 10.6 - Prob. 2OECh. 10.6 - Prob. 3OECh. 10.6 - Prob. 4OECh. 10.6 - Prob. 5OECh. 10.6 - Prob. 6OECh. 10.6 - Prob. 7OECh. 10.6 - Prob. 8OECh. 10.6 - Prob. 9OECh. 10.6 - Prob. 10OECh. 10.6 - Prob. 11OECh. 10.6 - Prob. 12OECh. 10.6 - Prob. 13OECh. 10.6 - Prob. 14OECh. 10.6 - Prob. 15OECh. 10.6 - Prob. 16OECh. 10.6 - Prob. 1WECh. 10.6 - Prob. 2WECh. 10.6 - Prob. 3WECh. 10.6 - Prob. 4WECh. 10.6 - Prob. 5WECh. 10.6 - Prob. 6WECh. 10.6 - Prob. 7WECh. 10.6 - Prob. 8WECh. 10.6 - Prob. 9WECh. 10.6 - Prob. 10WECh. 10.6 - Prob. 11WECh. 10.6 - Prob. 12WECh. 10.6 - Prob. 13WECh. 10.6 - Prob. 14WECh. 10.6 - Prob. 15WECh. 10.6 - Prob. 16WECh. 10.6 - Prob. 17WECh. 10.6 - Prob. 18WECh. 10.6 - Prob. 19WECh. 10.6 - Prob. 20WECh. 10.6 - Prob. 21WECh. 10.6 - Prob. 22WECh. 10.6 - Prob. 23WECh. 10.6 - Prob. 24WECh. 10.6 - Prob. 25WECh. 10.6 - Prob. 26WECh. 10.6 - Prob. 27WECh. 10.6 - Prob. 28WECh. 10.6 - Prob. 29WECh. 10.6 - Prob. 30WECh. 10.6 - Prob. 31WECh. 10.6 - Prob. 32WECh. 10.6 - Prob. 33WECh. 10.6 - Prob. 34WECh. 10.6 - Prob. 35WECh. 10.6 - Prob. 36WECh. 10.6 - Prob. 37WECh. 10.6 - Prob. 38WECh. 10.6 - Prob. 39WECh. 10.6 - Prob. 40WECh. 10.6 - Prob. 41WECh. 10.6 - Prob. 42WECh. 10.7 - Prob. 1OECh. 10.7 - Prob. 2OECh. 10.7 - Prob. 3OECh. 10.7 - Prob. 4OECh. 10.7 - Prob. 1PCh. 10.7 - Prob. 2PCh. 10.7 - Prob. 3PCh. 10.7 - Prob. 4PCh. 10.7 - Prob. 5PCh. 10.7 - Prob. 6PCh. 10.7 - Prob. 7PCh. 10.7 - Prob. 8PCh. 10.7 - Prob. 9PCh. 10.7 - Prob. 10PCh. 10.7 - Prob. 11PCh. 10.7 - Prob. 12PCh. 10.7 - Prob. 13PCh. 10.7 - Prob. 14PCh. 10.7 - Prob. 15PCh. 10.7 - Prob. 16PCh. 10.7 - Prob. 17PCh. 10.7 - Prob. 18PCh. 10.7 - Prob. 19PCh. 10.7 - Prob. 20PCh. 10.7 - Prob. 21PCh. 10.7 - Prob. 22PCh. 10.7 - Prob. 1MRECh. 10.7 - Prob. 2MRECh. 10.7 - Prob. 3MRECh. 10.7 - Prob. 4MRECh. 10.7 - Prob. 5MRECh. 10.7 - Prob. 6MRECh. 10.7 - Prob. 7MRECh. 10.7 - Prob. 8MRECh. 10.7 - Prob. 9MRECh. 10.7 - Prob. 10MRECh. 10.7 - Prob. 11MRECh. 10.7 - Prob. 12MRECh. 10.8 - Prob. 1OECh. 10.8 - Prob. 2OECh. 10.8 - Prob. 3OECh. 10.8 - Prob. 4OECh. 10.8 - Prob. 5OECh. 10.8 - Prob. 6OECh. 10.8 - 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