AP PC Logarithms

Write in logarithmic form.
5² = 25

• log₅2 = 25
• log₂25 = 5
• log₂₅5 = 2
• log₅25 = 2

Write in exponential form.
log₂32 = 5

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

Rewrite log_vn = a in exponential form.

• v^a = n
• n^a = v
• vⁿ = a
• aⁿ = v

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

Condense the expression to a single logarithm.

16 log u + 4 log v

• log(u¹⁶v⁴)

• log(u⁴v⁴)

• log(u¹⁶/v⁴)

• log 64uv

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Rewrite as an exponential equation:

log(10,000)=4.

• e⁴=10,000

• 4^10,000=10

• 10⁴=10,000

• 0⁴=10

Use logarithm properties to condense the expression log b² + log d

• b² + d

• log b²d

• log2b + logd

• log(2bd)

What type of functions are logarithms the inverse of?

• Quadratic functions

• Linear functions

• Radical functions

• Exponential functions

In the equation log₉ 729=3 , what is the base?

• 9

• 729

• 3