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Logs Homework -- Sample Test

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides a sample test on logarithms.

Exercise 1

log 3 3 = log 3 3=

Exercise 2

log 3 9 = log 3 9=

Exercise 3

log 3 27 = log 3 27=

Exercise 4

log 3 30 = log 3 30=

(approximately)

Exercise 5

log 3 1 = log 3 1=

Exercise 6

log 3 ( 1 3 ) = log 3 ( 1 3 )=

Exercise 7

log 3 1 9 = log 3 1 9 =

Exercise 8

log 3 ( -3 ) = log 3 (-3)=

Exercise 9

log 9 3 = log 9 3=

Exercise 10

3log38= 3log38 size 12{3 rSup { size 8{"log" rSub { size 6{3} } 8} } } {}=

Exercise 11

log -3 9 = log -3 9=

Exercise 12

log 100,000 = log100,000=

Exercise 13

log 1100,000=log1100,000 size 12{ { {1} over {"100","000"} } } {}=

Exercise 14

ln e 3 = ln e 3 =

Exercise 15

ln 4 = ln4=

Exercise 16

Rewrite as a logarithm equation (no exponents): q z = p q z =p

Exercise 17

Rewrite as an exponent equation (no logs): log w g = j log w g=j

For exercises #18-22, assume that…

  • log 5 12 = 1.544 log 5 12=1.544
  • log 5 20 = 1.861 log 5 20=1.861

Exercise 18

log 5 240 = log 5 240=

Exercise 19

log 5 35= log 5 35 size 12{ left ( { {3} over {5} } right )} {}=

Exercise 20

log 5 1 2 3 = log 5 1 2 3 =

Exercise 21

log 5 352= log 5 352 size 12{ left ( { {3} over {5} } right ) rSup { size 8{2} } } {}=

Exercise 22

log 5 400 = log 5 400=

Exercise 23

Graph y = - log 2 x + 2 y=- log 2 x+2.

Exercise 24

What are the domain and range of the graph you drew in exercise #23?

Exercise 25

I invest $200 in a bank that pays 4% interest, compounded annually. So after y y years, I have 200 ( 1.04 ) y 200(1.04 ) y dollars in the bank. When I come back, I find that my account is worth $1000. How many years has it been? Your answer will be a formula with a log in it.

Exercise 26

The “loudness” of a sound is given by the formula L = 10 log I L=10logI, where L L is the loudness (measured in decibels), and I I is the intensity of the sound wave.

  • a. If the sound wave intensity is 10, what is the loudness?
  • b. If the sound wave intensity is 10,000, what is the loudness?
  • c. If the sound wave intensity is 10,000,000, what is the loudness?
  • d. What happens to the loudness every time the sound wave intensity multiplies by 1,000?

Exercise 27

Solve for x x.

ln ( 3 ) + ln ( x ) = ln ( 21 ) ln(3)+ln(x)=ln(21)

Exercise 28

Solve for x x.

log 2 ( x ) + log 2 ( x + 10 ) = log 2 ( 11 ) log 2 (x)+ log 2 (x+10)= log 2 (11)

Extra Credit:

Solve for x x. e x = (cabin) e x =(cabin)

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