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Nilai x yang memenuhi persamaan: lo g ( x 2 − 24 ) = lo g x + 7 lo g 15 16 ​ + 5 lo g 24 25 ​ + 3 lo g 80 81 ​ adalah ...

Nilai yang memenuhi persamaan:  adalah ...

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

jawaban yang benar adalah C.

Pembahasan

Ingat sifat pada persamaan bentuk logaritma yaitu dansifat pada bentuk logaritma yaitu Ingat syarat numerus pada bentuk logaritma yaitu .Sehingga Didapatkan nilai yaitu dan .Karena numerus pada bentuk logaritma harus positif maka nilai yang memenuhi adalah ,karena untuk maka hasil dari dan akan bernilai negatif. Jadi, dapat disimpulkan bahwa nilai yang memenuhi persamaan:adalah adalah . Oleh karena itu, jawaban yang benar adalah C.

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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