Introduction to Logarithms Practice

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

Convert log_b(a) to exponential form.

Back

The exponential form of log_b(a) is b^c = a, where c is the logarithm.

Front

What is the logarithmic identity log_b(b) = ?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is the logarithmic identity log_b(1) = ?

Back

log_b(1) = 0, because any number raised to the power of 0 is 1.

Front

Rewrite in exponential form: log_2(16) = 4

Back

2^4 = 16.

Front

Rewrite in exponential form: log_10(100) = 2

Back

10^2 = 100.

Front

What is the value of log_5(25)?

Back

log_5(25) = 2, because 5^2 = 25.

Front

Solve for x: 2^x = 8

Back

x = 3, because 2^3 = 8.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number.