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Pertanyaan

Jika b − c lo g a ​ = c − a lo g b ​ = a − b lo g c ​ ,tentukanlah a a ⋅ b b ⋅ c c .

Jika , tentukanlah .

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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dapat disimpulkan bahwa hasil dari adalah .

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 sehingga akan didapatkan Ingat sifat pada bentuk logaritma yaitu dan maka Didapatkan ,ingat sifat pada logaritma yaitu maka sehingga Jadi, dapat disimpulkan bahwa hasil dari adalah .

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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