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 base of a common logarithm?

Back

The base of a common logarithm is 10.

Front

What is the base of a natural logarithm?

Back

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

Front

State the product property of logarithms.

Back

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

Front

State the quotient property of logarithms.

Back

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

Front

State the power property of logarithms.

Back

The power property states that log_b(x^k) = k * log_b(x).

Front

Expand log_b(xy).

Back

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

Front

Expand log_b(x/y).

Back

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

Front

Condense log_b(x) + log_b(y).

Back

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

Front

Condense log_b(x) - log_b(y).

Back

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