Logs and Exponential Form

Convert x⁴ = 81 to a Log

• Log₈₁(x) = 4

• Log₄(81) = x

• Log_x(81) = 4

• Log₄(x) = 81

Convert Log_a(100) = 2 to an exponent

• 100² = a

• 2^a = 100

• a² = 100

• a¹⁰⁰ = 2

Rewrite 3⁴ = 81 in logarithmic form.

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

Match each logarithmic expression to its equivalent exponential form.

• 10⁵ = x

• log₅ 10 = x

• x¹⁰ = 5

• log_x 5 = 10

• 5^x = 10

• log x = 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

Write in logarithmic form:

a^b = c

• log _a c = b

• log _b c = a

• log _a b = c

• log _b a = c

Logarithms are the inverse of ___________.

• Trees
• Quadratics
• Square
• Exponential

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