Logs- Expand & Condense

Rewrite in exponential form.

log₆₄ (1/4) = -1/3

• (-1/3)⁶⁴ = 1/4

• 64^-1/3= 1/4

• (-1/3)^1/4 = 64

• (1/4)⁶⁴ = -1/3

Rewrite in exponential form.

log₁₆ (1/256) = -2

• (1/256)^-2 = 16

• (1/256)¹⁶ = -2

• (-2)¹⁶ = 1/256

• 16^-2 = 1/256

Rewrite in exponential form.

log₆ 36 = 2

• 36⁶ = 2

• 6³⁶ = 2

• 36² = 6

• 6² = 36

Rewrite in exponential form.

log₃ (1/27) = -3

• (1/27)³ = -3

• (1/27)^-3 = 3

• 3^1/27 = -3

• 3^-3 = 1/27

Rewrite in logarithmic form.

16² = 256

• log₂ 16 = 256

• log₂ 256 = 16

• log₁₆ 256 = 2

• log₂₅₆ 2 = 16

Rewrite in logarithmic form.

14² = 196

• log₂ 14 = 196

• log₁₄ 196 = 2

• log₂ 192 = 14

• log₁₉₆ 2 = 14

Rewrite in logarithmic form.

9^-2 = 1/81

• log₉ (1/81) = -2

• log₉ -2 = 1/81

• log_-2 9 = 1/81

• log_1/81 9 = -2

Rewrite in logarithmic form.

64^-1/2 - 1/8

• log₆₄ (1/8) = -1/2

• log_1/8 64 = -1/2

• log_-1/2 (1/8) = 64

• log₆₄ (-1/2) = 1/8

Evaluate.

log₂ (1/16)

• 1/32

• -1/4

• 1/4

• -4

Evaluate.

log₄16

• -1/2

• 2

• -2

• 1/2