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, in the expression log_b(a) = c, 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

Evaluate log_3(27).

Back

3

Front

Write log_2(32) in exponential form.

Back

2^5 = 32

Front

Write 2^-4 in logarithmic form.

Back

log_2(1/16) = -4

Front

Evaluate log_2(√2).

Back

1/2

Front

Solve for x: 3^x = 27.

Back

x = 3

Front

What is the product rule for logarithms?

Back

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

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

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