Evaluating Logarithms

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. It is expressed as log_b(a) = c, meaning b^c = a.

Front

What is the value of log_3(27)?

Back

3, because 3^3 = 27.

Front

What is the value of log_17(1)?

Back

0, because any number raised to the power of 0 equals 1.

Front

What is the value of log_2(16)?

Back

4, because 2^4 = 16.

Front

What is the value of log_16(8)?

Back

3/4, because 16^(3/4) = 8.

Front

What is the value of log_a(a)?

Back

1, because any number raised to the power of 1 equals itself.

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^p) = p * log_b(m).