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 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(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^k) = k * log_b(x).

Front

Convert log_5(25) to exponential form.

Back

5^2 = 25.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

Expand log_2(8) - log_2(4).

Back

log_2(8/4) = log_2(2) = 1.

Front

What is the value of log_3(3^4)?

Back

4, because the logarithm of a number to its own base is the exponent.

Front

Convert log_4(1/16) to exponential form.

Back

4^-2 = 1/16.