Log Basics

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

Evaluate log_5(25).

Back

2

Front

Use the change of base formula to evaluate log_4(32).

Back

5/2

Front

Rewrite log_9(x) = 2 in exponential form.

Back

9^2 = x

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4

Front

Use the change of base formula to rewrite log_3(64).

Back

log(64) / log(3)

Front

What is the base of a logarithm?

Back

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

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a

Front

What is the value of log_10(1000)?

Back

3