7.5 Laws of Logarithms

Front

What is the Power Rule of Logarithms?

Back

The Power Rule states that log_b(x^n) = n * log_b(x).

Front

How do you express log_b(x/y) using logarithmic properties?

Back

log_b(x/y) = log_b(x) - log_b(y).

Front

What is the Product Rule of Logarithms?

Back

The Product Rule states that log_b(xy) = log_b(x) + log_b(y).

Front

How do you simplify the expression 2log(x) + 3log(xy)?

Back

The expression simplifies to log(x^5 * y^3).

Front

What is the Quotient Rule of Logarithms?

Back

The Quotient Rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

Expand log_2(5x).

Back

log_2(5x) = log_2(5) + log_2(x).

Front

How do you combine log(12) + 2log(x) into a single logarithm?

Back

log(12) + 2log(x) = log(12x^2).

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 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 does log_b(1) equal?

Back

log_b(1) = 0 for any base b > 0.