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Tentukan nilai x yang memenuhi tiap persamaan berikut: a. 31​alog8−45​alog4−alog161​=alog x

Pertanyaan

Tentukan nilai x yang memenuhi tiap persamaan berikut:
a. 1 third to the power of straight a log 8 minus 5 over 4 to the power of straight a log 4 minus to the power of straight a log 1 over 16 equals to the power of straight a log space x

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

nilai x yang memenuhi 1 third to the power of straight a log 8 minus 5 over 4 to the power of straight a log 4 minus to the power of straight a log 1 over 16 equals to the power of straight a log space x adalah 4 square root of 2.

Pembahasan

Ingat sifat bentuk logaritma

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript straight a space straight b minus log presuperscript straight a space straight c end cell equals cell log presuperscript straight a space straight b over straight c end cell row cell log presuperscript straight a space straight b to the power of straight m end cell equals cell straight m times log presuperscript straight a space straight b end cell end table

dan sifat persamaan logaritma

log presuperscript straight a space f left parenthesis x right parenthesis equals log presuperscript straight a space straight b rightwards double arrow f left parenthesis x right parenthesis equals straight b

untuk a greater than 1

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third to the power of straight a log 8 minus 5 over 4 to the power of straight a log 4 minus to the power of straight a log 1 over 16 equals to the power of straight a log space x to the power of straight a log open parentheses 2 cubed close parentheses to the power of 1 third end exponent minus to the power of straight a log open parentheses 2 squared close parentheses to the power of 5 over 4 end exponent minus to the power of straight a log open parentheses 2 to the power of 4 close parentheses to the power of negative 1 end exponent equals to the power of straight a log space x to the power of straight a log 2 minus to the power of straight a log 2 to the power of 5 over 2 end exponent minus to the power of straight a log 2 to the power of negative 4 end exponent equals to the power of straight a log space x to the power of straight a log open parentheses fraction numerator 2 over denominator 2 to the power of 5 over 2 end exponent times 2 to the power of negative 4 end exponent end fraction close parentheses equals to the power of straight a log space x to the power of straight a log open parentheses 2 to the power of 1 minus 5 over 2 plus 4 end exponent close parentheses equals to the power of straight a log space x to the power of straight a log open parentheses 2 to the power of 5 over 2 end exponent close parentheses equals to the power of straight a log space x end cell row cell 2 to the power of 5 over 2 end exponent end cell equals x row cell 4 square root of 2 end cell equals x end table

Dengan demikian, nilai x yang memenuhi 1 third to the power of straight a log 8 minus 5 over 4 to the power of straight a log 4 minus to the power of straight a log 1 over 16 equals to the power of straight a log space x adalah 4 square root of 2.

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