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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 to the power of a times b to the power of b times c to the power of 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 1.

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 scriptbase log invisible function application b to the power of m end scriptbase presuperscript a equals m times scriptbase log invisible function application b end scriptbase presuperscript a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 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 end cell equals cell log invisible function application a to the power of a plus log invisible function application b to the power of b plus log invisible function application c to the power of c end cell row blank equals cell a times log invisible function application a plus b times log invisible function application b plus c times log invisible function application c end cell row blank equals cell a times k left parenthesis b minus c right parenthesis plus b times k left parenthesis c minus a right parenthesis plus c times k left parenthesis a minus b right parenthesis end cell row blank equals cell a times left parenthesis k b minus k c right parenthesis plus b times left parenthesis k c minus k a right parenthesis plus c times left parenthesis k a minus k b right parenthesis end cell row blank equals cell left parenthesis k a b minus k a c right parenthesis plus left parenthesis k b c minus k a b right parenthesis plus left parenthesis k a c minus k b c right parenthesis end cell row blank equals cell k a b minus k a c plus k b c minus k a b plus k a c minus k b c end cell row blank equals 0 end table

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

table attributes columnalign right center left columnspacing 0px end attributes row cell log invisible function application open parentheses a to the power of a times b to the power of b times c to the power of c close parentheses end cell equals 0 row cell 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 end cell equals cell log invisible function application 1 end cell row cell a to the power of a times b to the power of b times c to the power of c end cell equals 1 end table

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 1.

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