evaluate logarithms

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

Evaluate log_9(81).

Back

2, because 9^2 = 81.

Front

Rewrite the equation 6^2 = 36 in logarithmic form.

Back

log_6(36) = 2.

Front

Write log_2(1/8) in exponential form.

Back

2^(-3) = 1/8.

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8.

Front

Write 2^(-4) = 1/16 in logarithmic form.

Back

log_2(1/16) = -4.

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

How do you convert a logarithmic equation to an exponential equation?

Back

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

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.