Logarithms

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. It is expressed as log_b(a) = c, meaning b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

Evaluate log_3(27).

Back

3

Front

Solve for x: log_x(25) = 2.

Back

5

Front

Write in exponential form: log_2(32) = 5.

Back

2^5 = 32

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8

Front

Write in logarithmic form: 5^2 = 25.

Back

log_5(25) = 2

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

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).