Logarithm Properties

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

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^n) = n * log_b(m).

Front

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

Back

log_b(x^6 / y^3).

Front

How do you express log(30) - log(6) as a single logarithm?

Back

log(30 / 6) = log(5).

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

What is the value of log_5(25)?

Back

2, because 5^2 = 25.