Nilai x yang memenuhi persamaan: log(x2−24)=logx+7log1516​+5log2425​+3log8081​ adalah ...

Pertanyaan

Nilai x yang memenuhi persamaan: log invisible function application left parenthesis x squared minus 24 right parenthesis equals log invisible function application x plus 7 log invisible function application 16 over 15 plus 5 log invisible function application 25 over 24 plus 3 log invisible function application 81 over 80 adalah ...

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat sifat pada persamaan bentuk logaritma yaitu scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript a equals scriptbase log invisible function application g left parenthesis x right parenthesis end scriptbase presuperscript b rightwards arrow f open parentheses x close parentheses equals g left parenthesis x right parenthesis dan 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 b c end scriptbase presuperscript a
  • 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

Ingat syarat numerus pada bentuk logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu b greater than 0. Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell log invisible function application open parentheses x squared minus 24 close parentheses end cell equals cell log invisible function application x plus 7 log invisible function application 16 over 15 plus 5 log invisible function application 25 over 24 plus 3 log invisible function application 81 over 80 end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application x plus log invisible function application open parentheses 16 over 15 close parentheses to the power of 7 plus log invisible function application open parentheses 25 over 24 close parentheses to the power of 5 plus log invisible function application open parentheses 81 over 80 close parentheses cubed end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times open parentheses 16 over 15 close parentheses to the power of 7 times open parentheses 25 over 24 close parentheses to the power of 5 times open parentheses 81 over 80 close parentheses cubed close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times open parentheses fraction numerator 2 to the power of 4 over denominator 3 times 5 end fraction close parentheses to the power of 7 times open parentheses fraction numerator 5 squared over denominator 8 times 3 end fraction close parentheses to the power of 5 times open parentheses fraction numerator 3 to the power of 4 over denominator 16 times 5 end fraction close parentheses cubed close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times open parentheses fraction numerator 2 to the power of 4 over denominator 3 times 5 end fraction close parentheses to the power of 7 times open parentheses fraction numerator 5 squared over denominator 2 cubed times 3 end fraction close parentheses to the power of 5 times open parentheses fraction numerator 3 to the power of 4 over denominator 2 to the power of 4 times 5 end fraction close parentheses cubed close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times fraction numerator 2 to the power of 28 over denominator 3 to the power of 7 times 5 to the power of 7 end fraction times fraction numerator 5 to the power of 10 over denominator 2 to the power of 15 times 3 to the power of 5 end fraction times fraction numerator 3 to the power of 12 over denominator 2 to the power of 12 times 5 cubed end fraction close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times fraction numerator 2 to the power of 28 times 3 to the power of 12 times 5 to the power of 10 over denominator 2 to the power of 27 times 3 to the power of 12 times 5 to the power of 10 end fraction close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times 2 to the power of 28 over 2 to the power of 27 close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application open parentheses x times 2 close parentheses end cell row cell log invisible function application left parenthesis x squared minus 24 right parenthesis end cell equals cell log invisible function application 2 x end cell row cell x squared minus 24 end cell equals cell 2 x end cell row cell x squared minus 2 x minus 24 end cell equals 0 row cell left parenthesis x minus 6 right parenthesis left parenthesis x plus 4 right parenthesis end cell equals 0 row cell x minus 6 end cell equals cell 0 blank atau blank x plus 4 equals 0 end cell row x equals cell 6 blank atau blank x equals negative 4 end cell end table

Didapatkan nilai x yaitu x equals 6 dan x equals negative 4. Karena numerus pada bentuk logaritma harus positif maka nilai x yang memenuhi adalah x equals 6, karena untuk x equals negative 4 maka hasil dari x squared minus 24 dan 2 x akan bernilai negatif. 

Jadi, dapat disimpulkan bahwa nilai x yang memenuhi persamaan: adalah log invisible function application left parenthesis x squared minus 24 right parenthesis equals log invisible function application x plus 7 log invisible function application 16 over 15 plus 5 log invisible function application 25 over 24 plus 3 log invisible function application 81 over 80 adalah x equals 6.

Oleh karena itu, jawaban yang benar adalah C.

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