Properties of Logarithms

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, in the expression log_b(a) = c, b^c = a.

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 base of the common logarithm?

Back

The base of the common logarithm is 10.

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e (approximately 2.718).

Front

Expand the expression: log_b(mn)

Back

log_b(m) + log_b(n) (Product Property of Logarithms).

Front

Expand the expression: log_b(m/n)

Back

log_b(m) - log_b(n) (Quotient Property of Logarithms).

Front

Expand the expression: log_b(m^k)

Back

k * log_b(m) (Power Property of Logarithms).

Front

Convert to exponential form: log_6(36) = 2

Back

6^2 = 36.

Front

Condense the expression: log_8(a) + log_8(b)

Back

log_8(ab) (Product Property of Logarithms).

Front

Condense the expression: 3log_8(a)

Back

log_8(a^3) (Power Property of Logarithms).