AP PC Logarithms

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

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

• 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)

Rewrite in exponential form:
ln(2) = x

• 2^x = 10

• 10² = x

• e^x = 2

• e² = x

Rewrite e^x = 9 using a logarithm

• ln x = 9

• ln 9 = x

• log_x e = 9

• log₉ x = e

ln(9x-2)=ln(x+14)

• x=2

• x=.156

• x=-3

• x=0