Logarithms (writing and solving)

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Write in exponential form

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Write in logarithmic form

2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4

• log_-4(¹/₁₆) = 2

• log _-4 2 = ¹/₁₆

• log₂(-4) = ¹/₁₆

Rewrite 3⁴ = 81 in logarithmic form.

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

Solve for x:
log_x 25 = 2

• 5
• -5
• 1/5
• -1/5

Solve for x.
3^x = 27

• 2
• 4
• 3
• 5

State the property (s) used to simplify the expression

6log 2 = log 64

• Product Property

• Quotient Property

• Power Property

• Product and Power Property

State the property (s) used to simplify the expression

log₄20 - 3log₄x = log₄(20/x³)

• Power Property

• Quotient Property

• Quotient and Power Property

• Product and Power Property

Write the logarithm expression as a single logarithm

log₅4 + log₅3

• log₅7

• log₅12

• log₇5

• 3log₅4

Write the logarithm expression as a single logarithm

log₆25 - log₆5

• log₆125

• log₅20

• log₆5

• log₆30