EVALUATE LOGARITHMS WITHOUT USING CALCULATOR

Find :

Problem 1 :

log₃ 9

Solution :

= log₃ 9

= log₃ 3²

= 2 log₃ 3

= 2 (1)

= 2

Problem 2 :

log₂ 32

Solution :

= log₂ 32

= log₂ 2⁵

= 5 log₂ 2

= 5 (1)

= 5

Problem 3 :

log₂ √2

Solution :

= log₂ √2

= log₂ 2^1/2

= 1/2 log₂ 2

= 1/2 (1)

= 1/2

Problem 4 :

log₄ √2

Solution :

= log₄ √2

Problem 5 :

log₃ 3√3

Solution :

= log₃ 3√3

Problem 6 :

log₆ 1

Solution :

= log₆ 1

= 0

Problem 7 :

log₈ 8

Solution :

= log₈ 8

= 1

Problem 8 :

log₈ (1/8)

Solution :

= log₈ (1/8)

= log₈ 8^-1

= (-1) log₈ 8

= -1 × 1

= -1

Problem 9 :

log_1/8 (1/8)

Solution :

= log_1/8 (1/8)

= 1

Problem 10 :

log_√2 (1/√2)

Solution :

= log_√2 (1/√2)

= log_√2 √2^-1

= (-1) log_√2 √2

= -1 × 1

= -1

Problem 11 :

log₂ (1/√2)

Solution :

= log₂ (1/√2)

= log₂ 2^-1/2

= (-1/2) log₂ 2

= -1/2 × 1

= -1/2

Problem 12 :

log₈ (1/√2)

Solution :

= log₈ (1/√2)

= log₈ (1/2)^1/2

= log₈ (2)^-1/2