Finding Logs

Front

What is a logarithm?

Back

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

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

Evaluate log_4(1).

Back

0

Front

What is the logarithm of a number to the same base?

Back

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

Front

What is the logarithm of 1 in any base?

Back

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

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a.

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

Evaluate log_4(4).

Back

1

Front

What is the product rule for logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

log_b(m / n) = log_b(m) - log_b(n).