HW 3.2 Logarithmic Functions

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.

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert a logarithmic equation log_b(a) = c to exponential form, rewrite it as 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 to obtain a certain value.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

What is the logarithmic form of the equation 5^2 = 25?

Back

log_5(25) = 2.

Front

What is the asymptote of the function y = log_b(x)?

Back

The vertical asymptote is x = 0.

Front

What is the domain of the function y = log_b(x)?

Back

The domain is (0, ∞).

Front

What is the range of the function y = log_b(x)?

Back

The range is (-∞, ∞).

Front

What is the value of log_2(8)?

Back

log_2(8) = 3.

Front

How do you evaluate log_b(1)?

Back

log_b(1) = 0 for any base b > 0.