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HiSET Logarithmic Functions — practice questions

Explore 6 free Logarithmic Functions questions in HiSET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Logarithmic Functions questions and exercises with answers

Showing questions 1–6 of 6.

The statement y = log base a of x is equivalent to which exponential statement?Read the answer and worked solution →What is the domain of the logarithmic function y = log base a of x?Read the answer and worked solution →In the notation log x with no base written, which base is meant?Read the answer and worked solution →Find the exact value of log base 2 of one sixteenth.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

The statement y = log base a of x is equivalent to which exponential statement?

  1. y equals a to the power x
  2. a equals x to the power y
  3. x equals a to the power y
  4. a equals y to the power x
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Correct answer: C. x equals a to the power y

1. A logarithm is the exponent that the base must be raised to. 2. So y is the exponent, a is the base and x is the result. 3. Writing that as an exponential statement gives x equal to a to the power y. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_

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What is the domain of the logarithmic function y = log base a of x?

  1. Every positive number
  2. Every real number
  3. Every whole number
  4. Every negative number
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Correct answer: A. Every positive number

1. A logarithm asks what exponent the base needs in order to reach the input. 2. An allowed base raised to any power comes out positive, so only positive inputs can be reached. 3. The domain is therefore every positive number, and the graph never touches the vertical axis. 4. The range, by contrast, is every real number, since the exponent can be anything. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_

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In the notation log x with no base written, which base is meant?

  1. Base 2 is meant
  2. Base e is meant
  3. Base 1 is meant
  4. Base 10 is meant
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Correct answer: D. Base 10 is meant

1. A logarithm with no written base follows a standing convention. 2. That convention is base 10, and it is called the common logarithm. 3. Base e has its own short form written as ln, the natural logarithm. 4. So log x on its own means log base 10 of x. _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 FunctionsApplications of Quadratic EquationsExponential and Logarithmic EquationsQuadratic InequalitiesSquare Root PropertyEquations in Quadratic FormExponential Functions