Logs and Exponentials

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

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 relationship between exponents and logarithms?

Back

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

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

log_b(x^k) = k * log_b(x).

Front

How do you convert a logarithmic equation to exponential form?

Back

If log_b(a) = c, then it can be rewritten as b^c = a.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the value of log_5(25)?

Back

2, because 5^2 = 25.