Properties of logarithms

If 3^x = y, which of the following is true?

• log₃y = x
• log₃x = y
• log_xy = 3
• log_y3 = x

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

Write in exponential form.
log₂32 = 5

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

Rewrite 3⁴ = 81 in logarithmic form.

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

Solve for x
5^x = 17

• x = log₁₇5
• x = log 5 + log 17
• x = log₅17
• x = (log 5)/(log 17)

Expand

• A
• B
• C
• D

Expand

• A
• B
• C
• D

Expand

• log₈ x + log₈ y + log₈ z
• 5log₈ x + 5log₈ y + 5log₈ z
• log₈ xy + 5log₈ z
• log₈ x + log₈ y + 5log₈ z

Write as a single logarithm:

log(30)-log(6)

• -6log(30)

• log(24)

• log(-24)

• log(5)

Solve the equation for x.

• 32
• 25
• 1.66
• 512