Expanding and Condensing Logarithms

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 product rule of logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M).

Front

How do you condense the expression log_8(x^3) + log_8(y^9)?

Back

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

Front

How do you expand the expression 6log_4(u)?

Back

6log_4(u) can be expressed as log_4(u^6) using the power rule.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

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 does log_b(M + N) equal?

Back

log_b(M + N) does not equal log_b(M) + log_b(N). It is not a valid logarithmic identity.

Front

How do you condense log_8(x^3) - log_8(y^9)?

Back

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