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.

Tags

CCSS.HSF.BF.B.5

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.