Converting Logs to Exponents and Vice Versa

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

Write in exponential form.
log₂(¹/₈) = -3

• 2^-3 = ¹/₈
• 2^1/8 = -3
• -3² = ¹/₈
• -3^1/8 = 2

Rewrite 3⁴ = 81 in logarithmic form.

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

Write 10⁴= 10000 in logarithmic form.

• log₁₀ 4 = 10000
• log₁₀₀₀₀ 4 = 10
• log₁₀ 10000 = 4
• log₄ 10000 = 10

Write log₃ 81 = 4 in exponential form.

• 81⁴=3
• 81³=4
• 4³=81
• 3⁴=81

Write log₆ 216 = 3 in exponential form.

• 3⁶=216
• 6³=216
• 216⁶=3
• 3²¹⁶=6

Rewrite log _a b = c into exponential form.

• a^b = c

• a^c = b

• b^a = c

• c^b = a

Write in exponential form:

log ₃ 27 = 3

• 3³ = 27

• 3²⁷ = 3

• 1³⁶ = 0

• 1⁰ = 36

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t