Logarithm Properties

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means that b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the product property of logarithms?

Back

The product property states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power property of logarithms?

Back

The power property states that log_b(xⁿ) = n * log_b(x).

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log₁₀(100)?

Back

log₁₀(100) = 2, because 10² = 100.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log₂(8)?

Back

log₂(8) = 3, because 2³ = 8.

Tags

CCSS.HSF.BF.B.5

Front

What is the logarithm of 1 in any base?

Back

log_b(1) = 0 for any base b > 0.

Front

What is the logarithm of the base itself?

Back

log_b(b) = 1 for any base b > 0.