Unit 2B: AP Precalculus Exp., Log., and Inverse Functions

Front

What is the value of k if the equation is satisfied?

Back

k = 27

Front

Solve for x: ln(3x) + ln(2x) = 3. Round to two decimal places.

Back

x = 1.83

Front

If f(x) = log_3(x), find x when f(x) = 4.

Back

x = 81

Front

What is the inverse of the function f(x) = log_4(x)?

Back

f^{-1}(x) = 4^x

Front

Condense the expression: \frac{1}{2}log(81) - \frac{1}{3}log(27 = log(______)

Back

log(3)

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

What is the change of base formula for logarithms?

Back

log_b(a) = \frac{log_k(a)}{log_k(b)} for any base k.

Front

What is the relationship between exponential and logarithmic functions?

Back

If y = b^x, then x = log_b(y).

Front

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

Back

The domain is x > 0.

Front

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

Back

The range is all real numbers.