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Jika 2log(x2−7)=alogbc+11​+blogac+11​+clogab+11​ maka x=…

Pertanyaan

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 horizontal ellipsis

  1. 1

  2. 2

  3. 3

  4. plus-or-minus 2

  5. plus-or-minus 3

Pembahasan Soal:

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

  • scriptbase log invisible function application a end scriptbase presuperscript a equals 1
  • 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 b c end scriptbase presuperscript a
  • 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 

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses x squared minus 7 close parentheses end scriptbase presuperscript 2 end cell equals 1 row cell 2 to the power of 1 end cell equals cell x squared minus 7 end cell row 2 equals cell x squared minus 7 end cell row cell 2 plus 7 end cell equals cell x squared end cell row 9 equals cell x squared end cell row cell square root of 9 end cell equals x row cell plus-or-minus 3 end cell equals x end table

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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 06 Oktober 2021

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