Logarithms Problems Workshop 5

Question 1

Sketch the graph of the function y = 3^x

Answer 1

Exponential growth function

Question 2

Sketch the graph of the function y = -3^x

Answer 2

Exponential decay function

Question 3

Sketch the graph of the function y = 3^x + 2

Answer 3

Exponential growth function translated upward by 2

Question 4

Convert log10 1000 = 3 to exponential form

Answer 4

10^3 = 1000

Question 5

Convert log3 9 = 2 to exponential form

Answer 5

3^2 = 9

Question 6

Convert log2 0.125 = -3 to exponential form

Answer 6

2^(-3) = 0.125

Question 7

Convert log10 1 = 0 to exponential form

Answer 7

10^0 = 1

Question 8

Convert log7 1 = -1 to exponential form

Answer 8

7^(-1) = 1

Question 9

Convert 72 = 49 to logarithmic form

Answer 9

log7(49) = 2

Question 10

Convert 25 = 32 to logarithmic form

Answer 10

log2(32) = 5

Question 11

Evaluate log5 125

Answer 11

3

Question 12

Evaluate log10 10000

Answer 12

4

Question 13

Evaluate log9 1

Answer 13

0

Question 14

Evaluate log7 7

Answer 14

1

Question 15

Evaluate log3 -3

Answer 15

undefined

Question 16

Evaluate log10 0.1

Answer 16

-1

Question 17

Evaluate log3 1/27

Answer 17

-3

Question 18

Evaluate log1 4 16

Answer 18

-2

Question 19

Simplify log5 + log2

Answer 19

log(5 * 2)

Question 20

Simplify log8 - log2

Answer 20

log(8/2)

Question 21

Simplify 3log2 - 2log3

Answer 21

log(2^3 / 3^2)

Question 22

Simplify log3 81 + log39 - log327

Answer 22

log(3^4 * 9 / 27)

Question 23

Simplify log√(xy) + 1/2 log(xy) - log(xy)

Answer 23

0

Question 24

Simplify log2 16 + log24 + log28

Answer 24

log(16 * 24 * 28)

Question 25

Evaluate 10^-2

Answer 25

1/100

Question 26

Evaluate 81^(1/3)

Answer 26

3

Question 27

Evaluate 2 - log4(3)

Answer 27

log4(16/3)

Question 28

Evaluate log(7) - log(4)

Answer 28

log(7/4)

Question 29

Evaluate log4(3) - 2

Answer 29

log4(3) - log4(16)