Logarithms Flashcard Review

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, if b^y = x, then log_b(x) = y.

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, allowing you to convert logarithms to a different base.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n). This means the logarithm of a product is the sum of the logarithms.

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n). This means the logarithm of a quotient is the difference of the logarithms.

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(m^p) = p * log_b(m). This means the logarithm of a number raised to a power is the power times the logarithm of the number.

Front

What does it mean for a logarithm to be undefined?

Back

A logarithm is undefined if its argument (the number you are taking the log of) is less than or equal to zero, or if the base is less than or equal to zero or equal to one.

Front

How do you solve an equation involving logarithms?

Back

To solve an equation involving logarithms, you can use properties of logarithms to combine or simplify the logs, then exponentiate to eliminate the logarithm.

Front

What is the relationship between exponents and logarithms?

Back

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

Front

How do you evaluate log_64(4)?

Back

To evaluate log_64(4), you can express 4 as 64^(1/3), so log_64(4) = 1/3.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.