Pertanyaan

Nilai x yang memenuhi persamaan adalah ….

Nilai x yang memenuhi persamaan $begin mathsize 14px style log presubscript presuperscript cube root of 3 square root of 3 end root end presuperscript invisible function application x equals fraction numerator 1 over denominator log presubscript presuperscript 2 invisible function application 18 minus log presubscript presuperscript 2 invisible function application 6 end fraction end style$ adalah ….

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Ingat sifat logaritma berikut ini. Maka dengan menyederhanakan ruas kiri kemudian ruas kanan persamaan di atas maka diperoleh, Kemudian syarat numerus persamaan diatas adalah x>0. Karena memenuhi syarat numerus tersebut maka nilai x yang memenuhi persamaan adalah .

Ingat sifat logaritma berikut ini.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript presuperscript a to the power of m end presuperscript invisible function application b end cell equals cell 1 over m times log presubscript presuperscript a invisible function application b end cell row cell n times log presubscript presuperscript a invisible function application b end cell equals cell log presubscript presuperscript a invisible function application b to the power of n end cell row cell log presubscript presuperscript a invisible function application x minus log presubscript presuperscript a invisible function application y end cell equals cell log presubscript presuperscript a invisible function application open parentheses x over y close parentheses end cell row cell fraction numerator 1 over denominator log presubscript presuperscript a invisible function application b end fraction end cell equals cell log presubscript presuperscript b invisible function application a end cell end table end style$

Maka dengan menyederhanakan ruas kiri kemudian ruas kanan persamaan di atas maka diperoleh,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript cube root of 3 square root of 3 end root end presuperscript invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell log presubscript blank presuperscript 3 to the power of 1 third end exponent 3 to the power of 1 over 9 end exponent end presuperscript invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell 3 to the power of open parentheses 1 third plus 1 over 9 close parentheses end exponent log invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell log presubscript blank presuperscript 3 to the power of 4 over 9 end exponent end presuperscript invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell fraction numerator 1 over denominator 4 over 9 end fraction times log presubscript blank presuperscript 3 invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell 9 over 4 times log presubscript blank presuperscript 3 invisible function application x end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 minus log presubscript blank presuperscript 2 invisible function application 6 end fraction end cell row cell log presubscript blank presuperscript 3 invisible function application x to the power of 9 over 4 end exponent end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 18 over 6 end fraction end cell row cell log presubscript blank presuperscript 3 invisible function application x to the power of 9 over 4 end exponent end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript 2 invisible function application 3 end fraction end cell row cell log presubscript blank presuperscript 3 invisible function application x to the power of 9 over 4 end exponent end cell equals cell log presubscript blank presuperscript 3 invisible function application 2 end cell row cell x to the power of 9 over 4 end exponent end cell equals 2 row x equals cell 2 to the power of 4 over 9 end exponent end cell end table end style$

Kemudian syarat numerus persamaan diatas adalah x>0. Karena memenuhi syarat numerus tersebut maka nilai x yang memenuhi persamaan adalah .