Pertanyaan

Jika 2 lo g ( x 2 − 7 ) = a lo g b c + 1 1 + b lo g a c + 1 1 + c lo g ab + 1 1 maka x = …

Jika $^{2} lo g (x^{2} - 7) = \frac{1}{^{a} lo g b c + 1} + \frac{1}{^{b} lo g a c + 1} + \frac{1}{^{c} lo g ab + 1}$ maka $x = \dots$

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat bentuk umum atau definisi dari logaritma yaitu dan sifat pada logaritma yaitu Maka perhitungannya sebagai berikut. Didapatkan ,sehingga Jadi, dapat disimpulkan bahwa jika maka . Oleh karena itu, jawaban yang benar adalah E.

Ingat bentuk umum atau definisi dari logaritma yaitu scriptbase log invisible function application b end scriptbase presuperscript a equals c rightwards arrow a to the power of c equals b dan sifat pada logaritma yaitu

$fraction numerator 1 over denominator scriptbase log invisible function application b end scriptbase presuperscript a end fraction equals scriptbase log invisible function application a end scriptbase presuperscript b$

Maka perhitungannya sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 end cell equals cell fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus 1 end fraction end cell row blank equals cell fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus scriptbase log invisible function application a end scriptbase presuperscript a end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus scriptbase log invisible function application b end scriptbase presuperscript b end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus scriptbase log invisible function application c end scriptbase presuperscript c end fraction end cell row blank equals cell fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript a end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript b end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript c end fraction end cell row blank equals cell scriptbase log invisible function application a end scriptbase presuperscript a b c end presuperscript plus scriptbase log invisible function application b end scriptbase presuperscript a b c end presuperscript plus scriptbase log invisible function application c end scriptbase presuperscript a b c end presuperscript end cell row blank equals cell scriptbase log invisible function application a b c end scriptbase presuperscript a b c end presuperscript end cell row blank equals 1 end table$

Didapatkan scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 equals 1 , sehingga

Jadi, dapat disimpulkan bahwa jika $scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 equals fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus 1 end fraction$ maka blank x equals plus-or-minus 3 .

Oleh karena itu, jawaban yang benar adalah E.