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, if b^y = x, then log_b(x) = y.

Tags

CCSS.HSF.BF.B.5

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 product property of logarithms?

Back

The product property states that log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^p) = p * log_b(m).

Front

How do you simplify log_b(a^p)?

Back

You can simplify log_b(a^p) to p * log_b(a) using the power property.

Front

What is the value of log_b(b)?

Back

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

Front

What is the value of log_b(1)?

Back

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

Front

How do you condense the expression log(a) - log(b)?

Back

You can condense it to log(a/b) using the quotient property.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Tags

CCSS.HSF.BF.B.5