Logarithms

Front

What is 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 base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

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 convert a logarithmic expression to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the value of log_3(9)?

Back

log_3(9) = 2 because 3^2 = 9.

Front

What is the value of log_2(32)?

Back

log_2(32) = 5 because 2^5 = 32.

Front

How do you simplify log_3(9) + log_3(27)?

Back

log_3(9) + log_3(27) = log_3(9 * 27) = log_3(243).

Front

What is the result of 2log(4) + log(2)?

Back

2log(4) + log(2) = log(4^2) + log(2) = log(16) + log(2) = log(32).