3.4B Logarithmic Equations

Write in exponential form.
log₂32 = 5

• 2^-5 = 32
• 2³² = 5
• 2⁵ = 32
• 32⁵ = 2

Convert 6^(x+2)=216 to logarithmic form

• log₂₁₆(x+2)=6
• log₆(x+2)=216
• log₆(216)=x+2
• log_(x+2)(216)=6

Convert 10^(x+5)=100 to logarithmic form.

• log₁₀₀=x+5
• log(x+5)=100
• log(100)=x+5
• log_(x+5)(100)=10

Convert log(x)=y+2 to exponential form.

• 10^(y+2)=x
• 1^x=y+2
• 10^x=y+2
• x^(y+2)=10

Solve for x:
log₄ x = 3

• 4
• 12
• 32
• 64

log₅(4x-7)=log₅(x+5)

• 3
• 12
• 4
• 7

log₉(x)+log₉(x+2)=log₉(35)

• 5
• -7
• 5, -7
• -7, -13

log(216)=(x-4)log(6)

• 1
• 3
• 7
• 0

2log₅7 = 3x+1 log₅49

• 1
• -1
• 5
• 0

3^{2x – 6}  = 81

• x = log 4
• x = 5
• x = 4
• x = -1