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Pertanyaan

Nilai x yang memenuhi persamaan 5 to the power of 2 x end exponent minus 26 times 5 to the power of x greater than negative 25 adalah ...

  1. 0 less than x less than 2 

  2. 1 less than x less than 25 

  3. x less than 0 space atau space x greater than 2 

  4. x less than 0 space atau space x greater than 5 

  5. x less than 1 space atau space x greater than 25

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diasumsikan maksud soal adalah nilai x yang memenuhi pertidaksamaan 5 to the power of 2 x end exponent minus 26 times 5 to the power of x greater than negative 25

Ingat kembali bahwa 

bullet space Jika space straight a to the power of straight f left parenthesis straight x right parenthesis end exponent greater than straight a to the power of straight g left parenthesis straight x right parenthesis end exponent space maka space straight f left parenthesis straight x right parenthesis greater than straight g left parenthesis straight x right parenthesis bullet space straight a to the power of 0 equals 1 bullet space left parenthesis straight a to the power of straight m right parenthesis to the power of straight n equals straight a to the power of mn end exponent  

Ubah pertidaksamaan tersebut menjadi seperti berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of 2 x end exponent minus 26 times 5 to the power of x end cell greater than cell negative 25 end cell row cell left parenthesis 5 to the power of x right parenthesis squared minus 26 times 5 to the power of x plus 25 end cell greater than 0 end table 

Misal 5 to the power of x equals y maka

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 5 to the power of x right parenthesis squared minus 26 times 5 to the power of x plus 25 end cell greater than 0 row cell y squared minus 26 y plus 25 end cell greater than 0 row cell left parenthesis y minus 25 right parenthesis left parenthesis y minus 1 right parenthesis end cell greater than 0 end table 

Akar-akar dari persamaan kuadrat tersebut yaitu y equals 25 space atau space y equals 1 

Selanjutnya cari penyelesaiannya dengan uji titik berdasarkan titik y equals 25 space atau space y equals 1 

 

maka penyelesaiannya yaitu straight y less than 1 space atau space straight y greater than 25 space 

Selanjutnya substitusikan kembali nilai 5 to the power of x equals y sehingga 

untuk y less than 1 

table attributes columnalign right center left columnspacing 0px end attributes row y less than 1 row cell 5 to the power of x end cell less than 1 row cell 5 to the power of x end cell less than cell 5 to the power of 0 end cell row x less than 0 end table 

untuk y greater than 25 

table attributes columnalign right center left columnspacing 0px end attributes row y greater than 25 row cell 5 to the power of x end cell greater than 25 row cell 5 to the power of x end cell greater than cell 5 squared end cell row x greater than 2 end table 

Jadi, nilai x yang memenuhi pertidaksamaan 5 to the power of 2 x end exponent minus 26 times 5 to the power of x greater than negative 25 adalah x less than 0 space atau space x greater than 2 

Oleh karena itu, jawaban yang benar adalah C.

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