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Question

The minimum value of 2 log subscript 10 end subscript invisible function application x minus log subscript x end subscript invisible function application 0.01 comma blank x greater than 1, is

  1. 1  
  2. negative 1  
  3. 2  
  4. 1/2  

The correct answer is: 1/2


    Let y equals 2 log subscript 10 end subscript invisible function application x minus log subscript x end subscript invisible function application 0.01. Then,
    y equals 2 log subscript 10 end subscript invisible function application x minus log subscript x end subscript invisible function application 10 to the power of negative 2 end exponent

    rightwards double arrow y equals 2 log subscript 10 end subscript invisible function application x plus fraction numerator 2 over denominator log subscript 10 end subscript invisible function application x end fraction equals 2 open curly brackets log subscript 10 end subscript invisible function application x plus fraction numerator 1 over denominator log subscript 10 end subscript invisible function application x end fraction close curly brackets greater or equal than 4 open square brackets because x greater than 1 close square brackets

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