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

Convert log_3(4x) = 2 to exponential form.

Back

3^2 = 4x, which simplifies to 9 = 4x.

Front

Solve for x: log_3(4x) = 2.

Back

x = 9/4.

Front

What is the value of log_8(64)?

Back

x = 2, because 8^2 = 64.

Front

Convert log_2(1/8) = -3 to exponential form.

Back

2^-3 = 1/8.

Front

What is the value of log_5(25)?

Back

y = 2, because 5^2 = 25.

Front

Convert log_2(32) = 5 to exponential form.

Back

2^5 = 32.

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

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

Back

a = b^c.