Properties of 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 property of logarithms?

Back

The product property states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power property of logarithms?

Back

The power property states that log_b(x^n) = n * log_b(x).

Front

How do you express log_b(1)?

Back

log_b(1) = 0, because any base raised to the power of 0 equals 1.

Front

How do you express log_b(b)?

Back

log_b(b) = 1, because any base raised to the power of 1 equals itself.

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

If log_b(x) = 3, what is x in terms of b?

Back

x = b^3.

Front

If log_b(4) = 2, what is b?

Back

b = 4^(1/2) = 2.

Front

True or False: log_b(xy) = log_b(x) * log_b(y).

Back

False. The correct property is log_b(xy) = log_b(x) + log_b(y).