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

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_4(16).

Back

2

Front

Solve for x: log_x(25) = 2.

Back

5

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4

Front

Solve for x: 3^x = 27.

Back

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).