Logarithms

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to produce a given number. For example, in log_b(a), b is the base.

Front

What is the logarithmic identity: log_b(b) = ?

Back

1, because any number raised to the power of 1 is itself.

Front

What is the logarithmic identity: log_b(1) = ?

Back

0, because any number raised to the power of 0 is 1.

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

How do you solve the equation 4^(2x + 1) = 17?

Back

x = 1.

Front

How do you solve the equation -6log_3(x - 3) = -24?

Back

x = 84.

Front

Evaluate log_5(5).

Back

1.

Front

Evaluate log_3(1/3).

Back

-1.

Front

How do you solve the equation -6log_{12}(x - 5) = -6?

Back

x = 17.