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Penyelesaian dari pertidaksamaan begin mathsize 14px style open parentheses log presubscript presuperscript a invisible function application x close parentheses squared plus 15 less than 8 times log presubscript presuperscript a invisible function application x end style dengan begin mathsize 14px style 0 less than a less than 1 end style adalah ....

  1. begin mathsize 14px style a to the power of 5 less than x less than a cubed end style

  2. begin mathsize 14px style a cubed less than x less than a to the power of 5 end style

  3. begin mathsize 14px style x less than a to the power of 5 space atau space space x greater than a cubed end style

  4. begin mathsize 14px style 0 less than x less than a cubed space atau space x greater than a to the power of 5 end style

  5. begin mathsize 14px style 0 less than x less than a to the power of 5 space text atau end text space x greater than a cubed end style 

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat bahwa nilai numerus dari suatu bentuk logaritma haruslah lebih dari 0.

Sehingga dari bentuk logaritma begin mathsize 14px style log presubscript presuperscript a invisible function application x end style didapat syarat bahwa

x > 0

Selain itu diketahui pula bahwa 0 < a < 1.

 

Perhatikan bahwa terdapat pertidaksamaan

undefined

Misalkan begin mathsize 14px style log presubscript presuperscript a invisible function application x equals k end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell k squared plus 15 end cell less than cell 8 k end cell row cell k squared minus 8 k plus 15 end cell less than 0 row cell open parentheses k minus 3 close parentheses open parentheses k minus 5 close parentheses end cell less than 0 end table end style

Didapat pembuat nol yaitu k = 3 atau k = 5.

Perhatikan garis bilangan berikut

Karena tanda pertidaksamaan yang digunakan adalah <, maka pilih daerah yang bernilai negatif, yaitu 3 < k < 5.

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 3 less than cell k less than 5 end cell row 3 less than cell log presubscript presuperscript a invisible function application x less than 5 end cell row cell log presubscript presuperscript a invisible function application a cubed end cell less than cell log presubscript presuperscript a invisible function application x less than log presubscript presuperscript a invisible function application a to the power of 5 end cell end table end style

Karena 0 < a < 1, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript presuperscript a invisible function application a cubed end cell less than cell log presubscript presuperscript a invisible function application x less than log presubscript presuperscript a invisible function application a to the power of 5 end cell row cell a cubed end cell greater than cell x greater than a to the power of 5 end cell row cell a to the power of 5 end cell less than cell x less than a cubed end cell end table end style 

Karena 0 < a < 1, maka begin mathsize 14px style a to the power of 5 end style sudah pasti lebih dari 0. Sehingga begin mathsize 14px style a to the power of 5 less than x less than a cubed end style sudah mencakup syarat x > 0. Maka penyelesaian dari pertidaksamaan begin mathsize 14px style open parentheses log presubscript presuperscript a invisible function application x close parentheses squared plus 15 less than 8 times log presubscript presuperscript a invisible function application x end style dengan 0 < a < 1 adalah begin mathsize 14px style a to the power of 5 less than x less than a cubed end style.

Jadi, jawaban yang tepat adalah A.

36

5.0 (3 rating)

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