Converting Logs and Exponents

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

Convert Log₂(64) = y to an exponent

• 64^y = 2

• 2⁶⁴ = y

• 64² = y

• 2^y = 64

Convert Log₃(x) = 4 to an exponent

• 3^x = 4

• 3⁴ = x

• x³ = 4

• 4^x = 3

Convert Log_a(100) = 2 to an exponent

• 100² = a

• 2^a = 100

• a² = 100

• a¹⁰⁰ = 2

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Evaluate log₄1

• 1
• 0
• 4
• undefined

Write the exponential equation as a logarithm
6³=216

• log₆(3) = 216
• log₃(6) = 216
• log₆(216)=3
• log₂₁₆(6)=3

log(x+6) = 1

• 4
• 4.222
• -5
• -9.550