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Diketahui 2log 5=b dan  5log 3=c, maka nilai dari8log (5+26​​−5−26​​)=...

Pertanyaan

Diketahui blank squared log space 5 equals b space dan space space to the power of 5 log space 3 equals c, maka nilai dariblank to the power of 8 log space open parentheses square root of 5 plus 2 square root of 6 end root minus square root of 5 minus 2 square root of 6 end root close parentheses equals... 

  1. 1 half 

  2. 1 third 

  3. 1 fourth 

  4. 1 fifth 

  5. 1 over 6 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat 

  • blank to the power of a to the power of m end exponent log space b to the power of n equals m over n times to the power of a log space b 
  • square root of open parentheses a plus b close parentheses plus-or-minus 2 square root of a b end root end root equals square root of a plus-or-minus square root of b 

Perhatikan perhitungan berikut 

blank to the power of 8 log space open parentheses square root of 5 plus 2 square root of 6 end root minus square root of 5 minus 2 square root of 6 end root close parentheses equals to the power of 8 log space open parentheses square root of open parentheses 3 plus 2 close parentheses plus 2 square root of 3 cross times 2 end root end root minus square root of open parentheses 3 plus 2 close parentheses minus 2 square root of 3 cross times 2 end root end root close parentheses equals to the power of 8 log space open square brackets open parentheses square root of 3 plus square root of 2 close parentheses minus open parentheses square root of 3 minus square root of 2 close parentheses close square brackets equals to the power of 8 log space open parentheses square root of 3 plus square root of 2 minus square root of 3 plus square root of 2 close parentheses equals to the power of 8 log space open parentheses 2 square root of 2 close parentheses equals to the power of 2 cubed end exponent log space 2 to the power of 3 over 2 end exponent equals fraction numerator begin display style 3 over 2 end style over denominator 3 end fraction times squared log space 2 equals 1 half times 1 equals 1 half 

Oleh karena itu, jawaban yang benar adalah A.

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