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

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.718.

Front

What is the common logarithm?

Back

The common logarithm is the logarithm with base 10, denoted as log(x) or log_10(x).

Front

How do you express log_b(x) + log_b(y) as a single logarithm?

Back

log_b(x) + log_b(y) can be expressed as log_b(xy) using the product property.

Front

How do you express log_b(x) - log_b(y) as a single logarithm?

Back

log_b(x) - log_b(y) can be expressed as log_b(x/y) using the quotient property.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.