Convert Between Exponential and Logarithmic Form

Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5

Rewrite in exponential form:

log₉x=2

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

Write 6^x = 8 in log form.

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

Write 5^x =10 in log form

• x = log 5

• x = log₅10

• x = 5 log10

• x = 10 log 5

Rewrite log₃t = 5 in exponential form.

• 5^t=3

• log₃5 = log₃t

• t⁵=3

• 3⁵=t

Rewrite log_vn = a in exponential form.

• v^a = n

• n^a = v

• vⁿ = a

• aⁿ = v

Write in logarithmic form:

a^b = c

• log _a c = b

• log _b c = a

• log _a b = c

• log _b a = c

Change to logarithmic form.

3^h = w

• log_w3 = h

• log₃w = h

• log_h3 = w

• log₃h = w

Convert 3^x = 12 to the equivalent log form.

• 3¹² = x

• log_x 3 = 12

• log₃ x = 12

• log₃ 12 = x

Change to exponential form.

log_a2 = 5

• a² = 5

• 5² = a

• a⁵ = 2

• 2⁵ = a