Deck 12: Section 1: Exponential and Logarithmic Functions

Question 1

Solve .

A)
B) {5}
C)
D)

Answer 1

Question 2

The level of sound in decibels (db) is given by the formula , where I is the sound intensity in watts per square meter. If the sound intensity of a jet airplane is 0.001 watts per square meter at a distance of 170 meters, what is the level of the sound at this point in db, rounded to the nearest tenth?

A) 74.7
B) 77.2
C) 90.0
D) 81.1

Answer 2

90.0

Question 3

Write log₉(28) - log₉(7) as a single logarithm.

A) 9³⁵
B) The logarithms cannot be combined.
C) log₉(4)
D) log₉(35)

Answer 3

log₉(4)

Question 4

Write log(16) in terms of log(4).

A) 2log(4)
B) The expression cannot be written in terms of log(4).
C) log(4) + 2
D) log₂(4)

Question 5

Write ln(r²) + ln(r⁴) + ln(r) as a single logarithm. Assume r represents numbers for which the logarithms are defined.

A) ln(r⁵)
B) ln(r⁷)
C) The logarithms cannot be combined.
D) ln(r⁸)

Question 6

Evaluate .

A)
B)
C)
D) 3

Question 7

Solve log(x) = 1.

A) {10}
B) {1}
C) no solution
D) {0.1}

Question 8

Rewrite as a single logarithm.

A)

B)

C) The expression cannot be written as a single logarithm.
D)

Question 9

Let . Find k(-3) rounded to 4 decimal places.

A) 0.0498
B) 0.1353
C) 7.3891
D) 0.7408

Question 10

Write log₈64 = 2 as an exponential equation.

A) 8² = 64
B) 8² = 8
C) 64² = 8
D) 64² = 64

Question 11

Simplify ln(e¹²).

A) 12
B) -12
C) e
D) 12 ln(e¹²)

Question 12

Rewrite in terms of log(3) and log(4).

A)

B)

C)

D)

Question 13

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 14

Let . Find g(-2).

A) 1
B) 8
C) 4
D) 2

Question 15

Solve:

A)
B) {2}
C)
D)

Question 16

If $7,000 is deposited in an account paying 5% compounded quarterly, then what amount will be in the account after 5 years?

A) $9,122.26
B) $6,998.26
C) $8,974.26
D) $18,573.08

Question 17

Solve -8^-6-x = -64.

A) {-8}
B) {0}
C) {-6}
D) {-7}

Question 18

Let . Solve for x.

A)
B) { }
C)
D) { }

Question 19

Write 2⁵ = 32 as a logarithmic equation.

A) log₂5 = 32
B) log₂32 = 2
C) log₅32 = 2
D) log₂32 = 5

Question 20

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 21

Solve log₃(x² - 1) = 2 + log₃(x² + 2).

A) {-2, 1}
B) Ø
C) {19}
D) {4, 7}

Question 22

Solve log₇(x - 24) + log₇(x + 24) = 2.

A) {26}
B) {-25}
C) {25}
D) {27}

Question 23

The number of grams of a radioactive substance in charcoal from an ancient campfire after t years is given by . If the sample has only 15 grams of radioactive substance, then when was the campfire used?

A) 5,752 years ago
B) 4,706 years ago
C) 12,040 years ago
D) 5,229 years ago

Question 24

Solve e^{x + 4} = 7.

A) {ln(7) - 4}
B) {ln(3)}
C) {4 ln(7)}
D) {ln(7) + 4}

Question 25

Evaluate log_1/3(3.6). Round to four decimal places.

A) -0.5064
B) -1.1660
C) 1.2809
D) -0.858