Unit 4 Flashcard

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n), where b is the base of the logarithm.

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n), where b is the base of the logarithm.

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(m^k) = k * log_b(m), where b is the base of the logarithm.

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

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

What is the value of log_b(b)?

Back

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

Front

What is the value of log_b(1)?

Back

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

Front

How do you simplify log_b(mn^k)?

Back

Using the product and power rules, log_b(mn^k) = log_b(m) + k * log_b(n).

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.