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Question

The value of 49 to the power of open parentheses 1 minus log subscript 7 end subscript invisible function application 2 close parentheses end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent is

  1. 27 divided by 2  
  2. 25 divided by 2  
  3. 625 divided by 16  
  4. None of these  

The correct answer is: 25 divided by 2


    49 to the power of open parentheses 1 minus log subscript 7 end subscript invisible function application 2 close parentheses end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent equals 49 cross times 7 to the power of negative 2 log subscript 7 end subscript invisible function application 2 end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent equals 49 cross times fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 50 over denominator 4 end fraction equals fraction numerator 25 over denominator 2 end fraction

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