Condensing & Expanding Logarithms

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n), where b is the base, and m and n are positive numbers.

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n), where b is the base, and m and n are positive numbers.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^k) = k * log_b(m), where b is the base, m is a positive number, and k is any real number.

Front

Expand: 6log_4(u) - 36log_4(v)

Back

6log_4(u) - 36log_4(v) is already in expanded form.

Front

Condense: log_8(x^6) - log_8(y^3)

Back

log_8(x^6/y^3) using the quotient rule.

Front

Expand: 6log_8(u) - 2log_8(v)

Back

6log_8(u) - 2log_8(v) is already in expanded form.

Front

Condense: 18log_8(a) - 3log_8(b)

Back

log_8(a^18/b^3) using the quotient and power rules.

Front

Condense: log_8(x^3) + log_8(y^9)

Back

log_8(x^3y^9) using the product rule.

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.