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 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

Evaluate: log_5(25)

Back

2

Front

Evaluate: log_3(81)

Back

4

Front

Write in exponential form: log_2(1/8) = -3

Back

2^-3 = 1/8

Front

What is the value of log(10^R)?

Back

R

Front

Evaluate: log_3(1/9)

Back

-2

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).