Basic Log Inverses

Find the inverse function:
f(x) = 5^x

• f ^-1(x) = log₅(x)

• f ^-1(x) = log_x(5)

• f ^-1(x) = 5^x

• f ^-1(x) = x⁵

Find the domain and range of:
f(x) = log₅(x)

• D: (-∞, ∞)
  R: (0, ∞)

• D: (-∞, ∞)
  R: (-∞, ∞)

• D: (0, ∞)
  R: (-∞, ∞)

• D: (-∞, 0)
  R: (-∞, ∞)

Find the inverse function:
f(x) = 2^x

• f ^-1(x) = log₂(x)

• f ^-1(x) = log_x(2)

• f ^-1(x) = 2^x

• f ^-1(x) = x²

A logarithmic function is the inverse of an exponential function. (a)  

• True

• False

What is the inverse of f(x)=5^x+3?

• f^-1(x)=log₃(x-5)

• f^-1(x)=log₅(x)-3

• f^-1(x)=log₅(x-3)

• f^-1(x)=log₅(x+3)

Find the inverse function:
f(x) = 10^x

• f ^-1(x) = log(x)

• f ^-1(x) = ln(x)

• f ^-1(x) = 10^x

• f ^-1(x) = x¹⁰

Find the domain and range of:
f(x) = log(x)

• D: all real numbers
  R: y > 0

• Domain: all real numbers
  Range: all real numbers

• Domain: x > 0
  Range: all real numbers

• Domain: all real numbers
  Range: y < 0

Find the inverse function:
f(x) = e^x

• f ^-1(x) = log(x)

• f ^-1(x) = ln(x)

• f ^-1(x) = e^x

• f ^-1(x) = x^e

Find the domain and range of:
f(x) = ln(x)

• D: all real numbers
  R: y > 0

• Domain: all real numbers
  Range: all real numbers

• Domain: x > 0
  Range: all real numbers

• Domain: all real numbers
  Range: y < 0

Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0

• Domain: all real numbers
  Range: all real numbers

• Domain: x > 0
  Range: all real numbers

• Domain: all real numbers
  Range: y < 0