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Introduction to Logarithmic Functions quiz

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  • What is a logarithm in terms of exponents and bases?
    A logarithm is the exponent that a base must be raised to in order to equal a particular number.
  • How do you write the logarithmic form of the equation 2^y = 10?
    The logarithmic form is y = log base 2 of 10.
  • What is the equivalent exponential form of y = log base 3 of 81?
    The equivalent exponential form is 3^y = 81.
  • If log base 5 of x = 3, what is the equivalent exponential equation?
    The equivalent exponential equation is 5^3 = x.
  • What is the inverse function of f(x) = 5^x?
    The inverse function is f⁻¹(x) = log base 5 of x.
  • What does the argument of a logarithm refer to?
    The argument is the number inside the log function, the value you are taking the logarithm of.
  • What is the value of log base b of b?
    log base b of b equals 1.
  • What is the value of log base b of 1 for any base b?
    log base b of 1 equals 0.
  • How can you evaluate log base 4 of 16 using properties of logarithms?
    Rewrite 16 as 4^2, so log base 4 of 16 = log base 4 of 4^2 = 2.
  • How do you evaluate log base 5 of 1/5?
    Rewrite 1/5 as 5^-1, so log base 5 of 1/5 = log base 5 of 5^-1 = -1.
  • What is the value of log base 10 of 10?
    log base 10 of 10 equals 1.
  • How do you convert the cube root of 4 into an exponent?
    The cube root of 4 can be written as 4^(1/3).
  • What is log base 4 of the cube root of 4?
    It is 1/3, since log base 4 of 4^(1/3) = 1/3.
  • What property allows logs and exponentials with the same base to 'cancel' each other?
    The inverse property: log base b of b^x = x and b^(log base b of x) = x.
  • When converting between exponential and logarithmic forms, what two parts should you focus on?
    Focus on the base and the exponent, as they determine the structure of both forms.