Evaluating Logarithmic Expressions and Forms

Front

What is 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

Evaluate: log_3(81)

Back

4, because 3^4 = 81.

Front

Solve for x: log_2(x) = 5

Back

x = 32, because 2^5 = 32.

Front

Evaluate: log_6(1/216)

Back

-3, because 6^-3 = 1/216.

Front

Write in logarithmic form: 5^2 = 25

Back

log_5(25) = 2.

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

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).

Front

What is the power rule for logarithms?

Back

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