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    Maths-
    General
    Easy

    Question

    t a greater than 1 be a real number. Then the number of roots equation a to the power of 2 log subscript 2 end subscript invisible function application x end exponent equals 5 plus 4 x to the power of log subscript 2 end subscript invisible function application a end exponent has

    1. 2  
    2. Infinite  
    3. 0  
    4. 1  

    The correct answer is: 1

      Given equation can be written as open parentheses a to the power of log subscript 2 end subscript invisible function application x end exponent close parentheses to the power of 2 end exponent equals 5 plus 4 blank a to the power of log subscript 2 end subscript invisible function application x end exponent
      Let a to the power of log subscript 2 end subscript invisible function application x end exponent equals t comma then the given equation is t to the power of 2 end exponent minus 4 t minus 5 equals 0. blankWe get open parentheses t minus 5 close parentheses open parentheses t plus 1 close parentheses equals 0
      rightwards double arrow t equals 5 blank o r blank t equals negative 1(rejecte(d)
      therefore a to the power of log subscript 2 end subscript invisible function application x end exponent equals 5 rightwards double arrow x to the power of log subscript 2 end subscript invisible function application a end exponent equals 5 rightwards double arrow x equals 5 to the power of log subscript a end subscript invisible function application 2 end exponent

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