Solving Log Equations

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

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 does log_b(b) equal?

Back

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

Front

What does log_b(1) equal?

Back

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

Front

How do you solve log_b(x) = c?

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

Tags

CCSS.HSF.BF.B.5

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 combine logarithms using the product property?

Back

To combine logarithms using the product property, use log_b(m) + log_b(n) = log_b(mn).