Logarithms

Front

What is 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 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

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

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

Front

How do you convert a logarithmic equation to an exponential equation?

Back

To convert log_b(a) = c to exponential form, use b^c = a.

Front

Evaluate: log_2(8)

Back

3, because 2^3 = 8.

Front

Evaluate: log_10(100)

Back

2, because 10^2 = 100.

Front

Write as one logarithm: log_4(16) + log_4(4)

Back

log_4(64), because log_4(16 * 4) = log_4(64).

Front

Solve for x: log_x(100) = 2

Back

10, because x^2 = 100.