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HiSET Properties of Logarithms — practice questions

Explore 3 free Properties of Logarithms questions in HiSET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Properties of Logarithms questions and exercises with answers

Showing questions 1–3 of 3.

What is the value of log base a of 1, for any allowed base a?Read the answer and worked solution →Judge each claim about the two graphsRead the answer and worked solution →Type the exponent each logarithm hidesRead the answer and worked solution →

Worked practice questions

What is the value of log base a of 1, for any allowed base a?

  1. It equals 0
  2. It equals 1
  3. It equals a
  4. It is undefined
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Correct answer: A. It equals 0

1. A logarithm answers the question of what exponent the base needs. 2. Any allowed base raised to the power 0 gives 1. 3. So the exponent needed to reach 1 is 0, which makes log base a of 1 equal to 0. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.4 Use the Properties of Logarithms_

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Judge each claim about the two graphs

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Questions
  1. Statement is true
    Yes
    Statement
    An exponential graph crosses the vertical axis at the point (0, 1).
  2. Statement is true
    No
    Statement
    An exponential graph dips below the horizontal axis for large inputs.
  3. Statement is true
    Yes
    Statement
    A logarithmic graph crosses the horizontal axis at the point (1, 0).
  4. Statement is true
    No
    Statement
    A logarithmic graph has a horizontal asymptote along the line y = 0.
  5. Statement is true
    Yes
    Statement
    The domain of a logarithmic function is every positive number.
  6. Statement is true
    No
    Statement
    The range of an exponential function is every real number.
Instructions
Tap true or false for each claim about exponential and logarithmic graphs.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_

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Type the exponent each logarithm hides

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Questions
  1. Answer
    3
    Question
    log base 2 of 8
  2. Answer
    2
    Question
    log base 5 of 25
  3. Answer
    0
    Question
    log base 3 of 1
  4. Answer
    1
    Question
    log base 7 of 7
  5. Answer
    3
    Question
    log base 4 of 64
  6. Answer
    -4
    Question
    log base 2 of 1/16
Instructions
Work it out and type the number.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_

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More Mathematics topics

The Quadratic FormulaGraphing Quadratic FunctionsLogarithmic FunctionsApplications of Quadratic EquationsExponential and Logarithmic EquationsQuadratic InequalitiesSquare Root PropertyEquations in Quadratic Form