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.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

What is the product property of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the quotient property of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the power property of logarithms?

Back

log_b(M^n) = n * log_b(M) for any positive number M and real number n.

Front

What is the definition of a natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.

Front

How do you express log_b(x) in terms of natural logarithms?

Back

log_b(x) = ln(x) / ln(b).

Front

What is the value of log_e(e)?

Back

log_e(e) = 1, because e raised to the power of 1 equals e.

Front

What is the value of log_b(1)?

Back

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

Front

What is the value of log_b(b)?

Back

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