Logarithm Properties

Front

When a logarithm has division inside of it, it expands using ________________.

Back

Subtraction

Front

Expand: 5log₅ a - 6log₅ b

Back

5log₅ a - 30log₅ b

Front

Write as a single log: log 12 + 2 log x

Back

log (12x²)

Front

What is the product property of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y)

Front

What is the quotient property of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y)

Front

What is the power property of logarithms?

Back

log_b(xⁿ) = n * log_b(x)

Front

Convert: log₁₀(1000) to exponential form.

Back

10³ = 1000

Front

If log₂(x) = 5, what is x?

Back

x = 2⁵ = 32

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Expand: log₃(9x)

Back

log₃(9) + log₃(x) = 2 + log₃(x) (since 9 = 3²)