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. For example, log_b(a) = c means b^c = a.

Front

Convert log_2(1/8) = -3 to exponential form.

Back

2^-3 = 1/8.

Front

Convert log_2(32) = 5 to exponential form.

Back

2^5 = 32.

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n).

Front

Convert 2^-4 = 1/16 to logarithmic form.

Back

log_2(1/16) = -4.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

Simplify log_2(800) - log_2(100).

Back

3.

Front

Simplify log_3(9) + log_3(27).

Back

5.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive k.