4.4 Properties of Logarithms (expand condense)

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 property of logarithms?

Back

The product property states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^p) = p * log_b(m).

Front

Expand the expression: log(3) + log(5)

Back

log(3 * 5) = log(15).

Front

Condense the expression: log(12) - log(4)

Back

log(12 / 4) = log(3).

Front

Write the expression as a single logarithm: log(2) + log(8) + log(4)

Back

log(2 * 8 * 4) = log(64).

Front

Write the expression as a single logarithm: 2 * log(3) + log(9)

Back

log(3^2) + log(9) = log(9) + log(9) = log(9 * 9) = log(81).

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 the expression: 3 * log(2) - log(4)

Back

log(2^3) - log(4) = log(8 / 4) = log(2).