Expanding and Condensing 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 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 M and N are positive numbers.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

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

Back

log_8(a^18/b^3) using the quotient rule.

Front

Expand log_4(u^6/v^36)

Back

6log_4(u) - 36log_4(v) using the quotient and power rules.

Front

Condense log_7(x) + log_7(y) + 4log_7(z)

Back

log_7(xy) + log_7(z^4) = log_7(xy*z^4) using the product rule.

Front

Expand log_5(a^5/b^30)

Back

5log_5(a) - 30log_5(b) using the quotient and power rules.

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

Condense log_8(x^6) + log_8(y^3)

Back

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