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Pertanyaan

Sederhanakan dan tentukan nilai dari bentuk berikut.

c. space to the power of 1 over 9 end exponent log space 1 third times to the power of 27 log space 49 times to the power of 1 over 7 end exponent log space 1 over 81 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari space to the power of 1 over 9 end exponent log space 1 third times to the power of 27 log space 49 times to the power of 1 over 7 end exponent log space 1 over 81 adalah 1 1 third.

Pembahasan

Ingat bahwa:

  • 1 over a to the power of b equals a to the power of negative b end exponent
  • blank to the power of a to the power of m end exponent log space b to the power of n equals n over m to the power of a log space b
  • blank to the power of a log space a equals 1
  • blank to the power of a log space b times blank to the power of b log space c equals blank to the power of a log space c 

Mencari nilai dari space to the power of 1 over 9 end exponent log space 1 third times to the power of 27 log space 49 times to the power of 1 over 7 end exponent log space 1 over 81:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space to the power of 1 over 9 end exponent log space 1 third times to the power of 27 log space 49 times to the power of 1 over 7 end exponent log space 1 over 81 end cell row blank equals cell space open parentheses blank to the power of 3 to the power of negative 2 end exponent end exponent log space 3 to the power of negative 1 end exponent close parentheses times open parentheses 2 over 3 times space cubed log space 7 close parentheses times open parentheses space to the power of 7 to the power of negative 1 end exponent end exponent log space 3 to the power of negative 4 end exponent close parentheses end cell row blank equals cell open parentheses fraction numerator negative 1 over denominator negative 2 end fraction blank cubed log space 3 close parentheses times open parentheses 2 over 3 times space cubed log space 7 close parentheses times open parentheses fraction numerator negative 4 over denominator negative 1 end fraction times space to the power of 7 log space 3 close parentheses end cell row blank equals cell fraction numerator negative 1 over denominator negative 2 end fraction times 2 over 3 times 4 times cubed log space 3 times space cubed log space 7 times space to the power of 7 log space 3 end cell row blank equals cell 4 over 3 times 1 times cubed log space 7 times space to the power of 7 log space 3 end cell row blank equals cell 4 over 3 times cubed log space 3 end cell row blank equals cell 4 over 3 times 1 end cell row blank equals cell 4 over 3 end cell row blank equals cell 1 space 1 third end cell end table    

Jadi, nilai dari space to the power of 1 over 9 end exponent log space 1 third times to the power of 27 log space 49 times to the power of 1 over 7 end exponent log space 1 over 81 adalah 1 1 third.

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