Converting and Solving Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another 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

Rewrite log_12(144) = 2 in exponential form.

Back

12^2 = 144.

Front

What is the value of log_32(4)?

Back

2/5.

Front

What is the value of log_3(27)?

Back

3.

Front

Rewrite log_4(1/64) = -3 in exponential form.

Back

4^-3 = 1/64.

Front

What is the value of log_16(8)?

Back

3/4.

Front

What does it mean if log_b(a) = 0?

Back

It means that a = 1, since any number raised to the power of 0 equals 1.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

If log_b(a) = c, what is the relationship between a, b, and c?

Back

a = b^c.