Roboguru

Pertanyaan

Diketahui bahwa 

blank cubed log space x times to the power of 6 log space x times to the power of 9 log space x equals cubed log space x times to the power of 6 log space x plus cubed log space x times to the power of 9 log space x plus to the power of 6 log space x times to the power of 9 log space x   

Tentukan nilai x (ada dua jawaban)

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

nilai x yang memenuhi persamaan di tersebut adalah  x equals 0 space atau space x equals 162

Pembahasan

Ingat 

  • blank to the power of a to the power of m end exponent log b equals 1 over m times space to the power of a log b
  •  blank to the power of a log space b equals fraction numerator blank to the power of c log space b over denominator blank to the power of c log space a end fraction 
  • blank to the power of a log space b equals fraction numerator 1 over denominator blank to the power of b log space a end fraction 
  • blank to the power of a log space f open parentheses x close parentheses equals b rightwards double arrow f open parentheses c close parentheses equals a to the power of c 

Perhatikan perhitungan berikut 

begin mathsize 12px style blank cubed log space x times to the power of 6 log space x times to the power of 9 log space x equals cubed log space x times to the power of 6 log space x plus cubed log space x times to the power of 9 log space x plus to the power of 6 log space x times to the power of 9 log space x cubed log space x times to the power of 6 log space x times to the power of 3 squared end exponent log space x equals cubed log space x times to the power of 6 log space x plus cubed log space x times to the power of 3 squared end exponent log space x plus to the power of 6 log space x times to the power of 3 squared end exponent log space x 1 half times cubed log space x times to the power of 6 log space x times cubed log space x equals cubed log space x times to the power of 6 log space x plus 1 half times cubed log space x times cubed log space x plus 1 half times to the power of 6 log space x times cubed log space x 1 half times open parentheses blank cubed log space x close parentheses squared times to the power of 6 log space x equals cubed log space x times to the power of 6 log space x plus 1 half times open parentheses blank cubed log space x close parentheses squared plus 1 half times to the power of 6 log space x times cubed log space x 1 half times blank cubed open parentheses log space x close parentheses squared times to the power of 6 log space x minus 1 half times open parentheses blank cubed log space x close parentheses squared equals cubed log space x times to the power of 6 log space x plus 1 half times to the power of 6 log space x times cubed log space x 1 half times blank cubed open parentheses log space x close parentheses squared times to the power of 6 log space x minus 1 half times open parentheses blank cubed log space x close parentheses squared equals 3 over 2 times cubed log space x times to the power of 6 log space x 1 half times blank cubed open parentheses log space x close parentheses squared times fraction numerator blank cubed log space x over denominator blank cubed log space 6 end fraction minus 1 half times open parentheses blank cubed log space x close parentheses squared equals 3 over 2 times cubed log space x times fraction numerator blank cubed log space x over denominator blank cubed log space 6 end fraction blank cubed open parentheses log space x close parentheses squared times fraction numerator blank cubed log space x over denominator blank cubed log space 6 end fraction minus open parentheses blank cubed log space x close parentheses squared equals 3 times cubed log space x times fraction numerator blank cubed log space x over denominator blank cubed log space 6 end fraction fraction numerator 1 over denominator blank cubed log space 6 end fraction times open parentheses blank cubed log space x close parentheses cubed minus open parentheses blank cubed log space x close parentheses squared equals fraction numerator 3 over denominator blank cubed log space 6 end fraction times open parentheses blank cubed log space x close parentheses squared  fraction numerator 1 over denominator blank cubed log space 6 end fraction times open parentheses blank cubed log space x close parentheses cubed minus open parentheses blank cubed log space x close parentheses squared minus fraction numerator 3 over denominator blank cubed log space 6 end fraction times open parentheses blank cubed log space x close parentheses squared equals 0 open parentheses blank cubed log space x close parentheses squared open parentheses fraction numerator blank cubed log space x over denominator blank cubed log space 6 end fraction minus 1 minus fraction numerator 3 over denominator blank cubed log space 6 end fraction close parentheses equals 0 open parentheses blank cubed log space x close parentheses squared open parentheses blank to the power of 6 log space 3 times cubed log space x minus 1 minus 3 times to the power of 6 log space 3 times close parentheses equals 0 end style 

Dari persamaan tersebut, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses blank cubed log space x close parentheses squared end cell equals cell 0 cubed log space x equals 0 end cell row x equals cell 3 to the power of 0 end cell row x equals 1 end table 

atau 

table attributes columnalign right center left columnspacing 0px end attributes row cell blank to the power of 6 log space 3 times cubed log space x minus 1 minus 3 times to the power of 6 log space 3 end cell equals cell 0 to the power of 6 log space 3 times cubed log space x equals 1 plus 3 times to the power of 6 log space 3 cubed log space x equals fraction numerator blank to the power of 6 log space 6 plus to the power of 6 log space 3 cubed over denominator blank to the power of 6 log space 3 end fraction cubed log space x equals fraction numerator blank to the power of 6 log 162 over denominator blank to the power of 6 log space 3 end fraction cubed log space x equals cubed log space 162 end cell row x equals 162 end table  

Dengan demikian, nilai x yang memenuhi persamaan di tersebut adalah  x equals 0 space atau space x equals 162

247

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