Logarithms and Natural Log Equations

Which of the following illustrates the Quotient Property of Logarithms

• log₄(x ÷ y) = log₄(x) - log₄(y)

• log₄(x ÷ y) = log₄(x) ÷ log₄(y)

• log₄(x - y) = log₄(x) ÷ log₄(y)

Which of the following illustrates the Power Property of Logarithms

• log₅(m)ⁿ = n + log₅(m)

• log₅(m)ⁿ = n ⋅ log₅(m)

• log₅(m)ⁿ = log₅(n ⋅ m)

Condense

• A

• B

• C

• D

Expand log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Write in logarithmic form:

a^b = c

• log _a c = b

• log _b c = a

• log _a b = c

• log _b a = c

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

Change to logarithmic form.

3^h = w

• log_w3 = h

• log₃w = h

• log_h3 = w

• log₃h = w