Properties of Logarithms

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

Front

What is the product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

How do you condense the expression log_a(x) + log_a(y)?

Back

You can condense it to log_a(xy) using the product property.

Front

How do you condense the expression log_a(x) - log_a(y)?

Back

You can condense it to log_a(x/y) using the quotient property.

Front

How do you expand the expression log_a(M^p)?

Back

You can expand it to p * log_a(M) using the power property.

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 value of log_b(b)?

Back

The value of log_b(b) is 1, because b^1 = b.

Front

What is the value of log_b(1)?

Back

The value of log_b(1) is 0, because b^0 = 1.