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, if b^y = x, then log_b(x) = y.

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

How do you condense the expression 6log_8(x) - 3log_8(y)?

Back

The expression can be condensed to log_8(x^6/y^3).

Front

How do you expand the expression log_b(MN)?

Back

Using the product rule, log_b(MN) = log_b(M) + log_b(N).

Front

How do you expand the expression log_b(M/N)?

Back

Using the quotient rule, log_b(M/N) = log_b(M) - log_b(N).

Front

How do you expand the expression log_b(M^p)?

Back

Using the power rule, log_b(M^p) = p * log_b(M).

Front

What is the expanded form of 5log_5(a) - 30log_5(b)?

Back

The expanded form is 5log_5(a) - 30log_5(b).

Front

Expand ln(w^3 * √u * v).

Back

The expansion is ln(w) + (3/2)ln(u) + ln(v).