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, log_b(a) = c means b^c = a.

Front

What is the base of the common logarithm?

Back

The base of the common logarithm is 10.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the product property of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the quotient property of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the power property of logarithms?

Back

log_b(M^p) = p * log_b(M) for any positive number M and any real number p.

Front

How do you condense the expression log_b(M) + log_b(N)?

Back

It can be condensed to log_b(MN) using the product property.

Front

How do you condense the expression log_b(M) - log_b(N)?

Back

It can be condensed to log_b(M/N) using the quotient property.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is the value of log_b(1)?

Back

log_b(1) = 0, because any number raised to the power of 0 is 1.