Logarithms Review

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, in the equation log_b(a) = c, b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

Rewrite the equation in exponential form: log_v(n) = a

Back

v^a = n.

Front

Write as one logarithm: log_3(9) + log_3(27)

Back

log_3(243) = 5.

Front

Rewrite the equation into logarithmic form: 6^2 = 36

Back

log_6(36) = 2.

Front

What is an exponential function?

Back

A function of the form f(x) = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

Evaluate the logarithm: log_3(27)

Back

3.

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(mn) = 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).