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Question : Evaluate the given logarithm by applying the appropriate rule : 2151534

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR.

1) Given log_{10}2 = 0.3010 and log_{10}3 = 0.4771, evaluate log_{10}6.

A) 0.7781

B) 0.9030

C) 0.1436

D) 0.9542

2) Given log_{10}2 = 0.3010 and log_{10}3 = 0.4771, evaluate log_{10}24.

A) 1.7323

B) 0.5044

C) 0.4308

D) 1.3801

3) Given log_{10}2 = 0.3010 and log_{10}3 = 0.4771, evaluate log_{10}24.

A) 1.7323

B) 0.5044

C) 1.3801

D) 0.4308

4) Given that log_{10}2 = 0.3010 and log_{10}3 = 0.4771, find log_{10}(9/8)

A) 0.8293

B) 0.0512

C) 0.1992

D) 2.0333

Decide whether the statement is true or false.

5) log_{3}(7 + 7) = log_{3}7 + log_{3}7

A) False

B) True

6) log_{7}(17 - 3) = log_{7}17 - log_{7}3

A) False

B) True

7) log_{2}2^{-1} + log_{2}2 = 0

A) True

B) False

8) log_{5}2 - log_{2}5 = 0

A) False

B) True

9) log_{6}60 - log_{6}10 = 1

A) False

B) True

10) (log_{8}10/log_{8}80) = (1/8)

A) True

B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

11) Give a definition for the following term: quotient rule of logarithms.

12) A student claims that since log_{b}x = a is not defined for negative values of x, then a must also not be negative. What is wrong with this statement?

13) Logarithms simplify calculations by changing multiplication to ___.

14) A classmate missed the lecture concerning the power rule of logarithms. When your classmate calls you on the phone for an explanation of why it works, what should you say to explain it?

15) Why is finding the value of log_{a}a^{6} like answering the question "What is the name of the girl whose name is Jane?"

16) Why is finding the value of a^{ }(log_{a12}) like answering the question "What is the name of the boy whose name is John?"

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

17) Use a property of logarithms to evaluate 3^{log}_{3}^{23}.

A) 23

B) (1/3)

C) (1/23)

D) 3

18) Use a property of logarithms to evaluate log_{8}8^{29}.

A) (1/29)

B) 29

C) (1/8)

D) 8

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

19) Explain how this statement needs to be changed so that it is true.

log_{3}(7 + 7) = log_{3}7 + log_{3}7

20) Explain why this sequence of steps is incorrect.

log_{3}100 = log_{3}[(-10)(-10)]

= log_{3}(-10) + log_{3}(-10)