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Nilai  yang memenuhi  adalah ...

Pertanyaan

Nilai x yang memenuhi 5 to the power of 2 x end exponent minus 6 times 5 to the power of x plus 1 end exponent plus 125 less than 0 adalah ...

  1. 5 less than x less than 25

  2. 5 less than x less than 15 

  3. 2 less than x less than 5

  4. 1 less than x less than 5 

  5. 1 less than x less than 2 

Pembahasan Soal:

Diketahui:

Pertidaksamaan 5 to the power of 2 x end exponent minus 6 times 5 to the power of x plus 1 end exponent plus 125 less than 0

Ditanya:

Nilai x

Pada pertidaksamaan eksponen yang dalam penyelesaiannya perlu direduksi terlebih dahulu, dan hasil reduksinya merupakan pertidaksamaan kuadrat. Pertidaksamaan eksponen tersebut mempunyai bentuk umum sebagai berikut.

a p to the power of 2 x end exponent plus b p to the power of x plus c greater than 0 

Perlu diingat bahwa:

k to the power of open parentheses l plus m close parentheses end exponent equals k to the power of l times k to the power of m open parentheses k to the power of l close parentheses to the power of m equals k to the power of l times m end exponent 

Perhatikan perhitungan berikut:

        table attributes columnalign right center left columnspacing 0px end attributes row cell space space 5 to the power of 2 x end exponent minus 6 times 5 to the power of x plus 1 end exponent plus 125 end cell less than 0 row cell open parentheses 5 to the power of x close parentheses squared minus 6 times 5 to the power of x times 5 to the power of 1 plus 125 end cell less than 0 row cell open parentheses 5 to the power of x close parentheses squared minus 30 times 5 to the power of x plus 125 end cell less than 0 row cell open parentheses 5 to the power of x minus 5 close parentheses open parentheses 5 to the power of x minus 25 close parentheses end cell less than 0 end table
           5 to the power of x minus 5 greater than 0 space atau space 5 to the power of x minus 25 less than 0 space 5 to the power of x greater than 5 space atau space 5 to the power of x less than 25 5 to the power of x greater than 5 to the power of 1 space atau space 5 to the power of x less than 5 squared x greater than 1 space atau space x less than 2 1 less than x less than 2

Sehingga, nilai x yang memenuhi 5 to the power of 2 x end exponent minus 6 times 5 to the power of x plus 1 end exponent plus 125 less than 0 adalah 1 less than x less than 2

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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