Practice: Rewriting and Evaluating 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, 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

What is the logarithmic identity log_b(b) = ?

Back

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

Front

What is the logarithmic identity log_b(1) = ?

Back

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

Front

How do you rewrite log_5(25) in exponential form?

Back

log_5(25) = 2 can be rewritten as 5^2 = 25.

Front

What is the value of log_3(81)?

Back

log_3(81) = 4, because 3^4 = 81.

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 rule for logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

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