Jika b−cloga=c−alogb=a−blogc, tentukanlah aa⋅bb⋅cc.

Pertanyaan

Jika $fraction numerator log invisible function application a over denominator b minus c end fraction equals fraction numerator log invisible function application b over denominator c minus a end fraction equals fraction numerator log invisible function application c over denominator a minus b end fraction$ , tentukanlah $a^a⋅b^b⋅c^c$ .

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

dapat disimpulkan bahwa hasil dari a to the power of a times b to the power of b times c to the power of c

adalah

Pembahasan

Untuk meyelesaikan soal perlu dilakukan permisalan sebagai berikut.

Misal $fraction numerator log invisible function application a over denominator b minus c end fraction equals fraction numerator log invisible function application b over denominator c minus a end fraction equals fraction numerator log invisible function application c over denominator a minus b end fraction equals k$ sehingga akan didapatkan

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log invisible function application a over denominator b minus c end fraction end cell equals k row cell log invisible function application a end cell equals cell k left parenthesis b minus c right parenthesis end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log invisible function application b over denominator c minus a end fraction end cell equals k row cell log invisible function application b end cell equals cell k left parenthesis c minus a right parenthesis end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log invisible function application c over denominator a minus b end fraction end cell equals k row cell log invisible function application c end cell equals cell k left parenthesis a minus b right parenthesis end cell end table$

Ingat sifat pada bentuk logaritma yaitu scriptbase log invisible function application b end scriptbase presuperscript a plus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application c end scriptbase presuperscript a dan maka

Didapatkan log invisible function application left parenthesis a to the power of a times b to the power of b times c to the power of c right parenthesis equals 0 , ingat sifat pada logaritma yaitu scriptbase log invisible function application b end scriptbase presuperscript a equals scriptbase log invisible function application c end scriptbase presuperscript a maka b equals c sehingga

Jadi, dapat disimpulkan bahwa hasil dari a to the power of a times b to the power of b times c to the power of c adalah .