Logarithms

Change to Logarithmic form:

3⁴ = 81

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3
• log ₃ 125 = 5
• log ₅ 3 =125
• log₁₂₅ 3 = 5

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Change to Exponential Form:
log₃ 81 = 4

• 81³ = 4
• 81⁴ = 3
• 3⁴ = 81
• 4³ =81

Change to Exponential Form:
log₂₈₉ 17 = 1/2

• 289^1/2 = 17
• 17^1/2 = 289
• 289¹⁷ = 1/2
• 1/2¹⁷ = 289

Convert 16 = 2^x to a Log

• Log₂(x) = 16

• Log₂(16) = x

• Log₁₆(x) = 2

• Log_x(16) = 2

Convert 4^x = 64 to a Log

• Log₆₄(x) = 4

• Log_x(64) = 4

• Log₄(64) = x

• Log₄(x) = 64

Convert y = 2⁵ to a Log

• Log₂(y) = 5

• Log₂(5) = y

• Log_y(2) = 5

• Log₅(y) = 2

Evaluate by thinking 4 to what power is 16, so

log₄16

• 2

• 4

• 1/2

• -2

True or False: log₈64=2

• True
• False