Pertanyaan

Jika 3 2 x − 1 = 6 x ⋅ 3 1 − x maka x = ...

Jika $3^{2 x - 1} = 6^{x} \cdot 3^{1 - x}$ maka $x =$ ...

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Diketahui : Ingat kembali bahwa : Sehingga Ubah bentuk eksponentersebut ke bentuk logaritma Ingat kembali bahwa : Sehingga Oleh karena itu, jawaban yang benar adalah D.

Diketahui : 3 to the power of 2 x minus 1 end exponent equals 6 to the power of x times 3 to the power of 1 minus x end exponent

Ingat kembali bahwa :

Sehingga

Ubah bentuk eksponen tersebut ke bentuk logaritma

Ingat kembali bahwa :

$bullet space log presuperscript straight a space f left parenthesis x right parenthesis equals log presuperscript straight a space g left parenthesis x right parenthesis rightwards arrow f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis bullet space log presuperscript straight a space straight b to the power of straight m equals straight m space log presuperscript straight a space straight b bullet space log presuperscript straight a space straight b minus log presuperscript straight a space straight c equals log presuperscript straight a space straight b over straight c bullet space fraction numerator log presuperscript straight p space straight b over denominator log presuperscript straight p space straight a end fraction equals log presuperscript straight a space straight b$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 2 x minus 2 end exponent end cell equals cell 2 to the power of x end cell row cell log space 3 to the power of 2 x minus 2 end exponent end cell equals cell log space 2 to the power of x end cell row cell left parenthesis 2 x minus 2 right parenthesis space log space 3 end cell equals cell x space log space 2 end cell row cell 2 x space log space 3 minus 2 space log space 3 end cell equals cell x space log space 2 end cell row cell 2 x space log space 3 minus x space log space 2 end cell equals cell 2 space log space 3 end cell row cell x left parenthesis 2 space log space 3 minus log space 2 right parenthesis end cell equals cell 2 space log space 3 end cell row cell x left parenthesis log space 3 squared minus log space 2 right parenthesis end cell equals cell log space 3 squared end cell row cell x left parenthesis log space 3 squared over 2 right parenthesis end cell equals cell log space 3 squared end cell row cell x left parenthesis log space 9 over 2 right parenthesis end cell equals cell log space 9 end cell row x equals cell fraction numerator log space 9 over denominator log space begin display style 9 over 2 end style end fraction end cell row x equals cell fraction numerator log space 9 over denominator log space 4 comma 5 end fraction end cell row x equals cell log presuperscript 4 comma 5 end presuperscript space 9 end cell end table$

Oleh karena itu, jawaban yang benar adalah D.