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Pertanyaan

( 3 ​ ) 9 l o g ( x − 1 ) 2 = ...

...

  1. open parentheses x minus 1 close parentheses to the power of 4

  2. open parentheses x minus 1 close parentheses squared 

  3. open parentheses x minus 1 close parentheses  

  4. square root of x minus 1 end root

  5. fourth root of x minus 1 end root

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R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

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Pembahasan

Perlu diingat bahwa: Perhatikan perhitungan berikut: Sehingga, bentuk sederhana dari adalah . Jadi, jawaban yang tepat adalah D.

Perlu diingat bahwa:

open parentheses a to the power of b close parentheses to the power of c equals a to the power of b times c end exponent log presuperscript a to the power of m end presuperscript space b to the power of n equals n over m times scriptbase log space b end scriptbase presuperscript a log presuperscript a space b to the power of c equals c times log presuperscript a space b a to the power of log presuperscript a space b end exponent equals b 

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 3 close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent end cell equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of log presuperscript 3 squared end presuperscript space open parentheses x minus 1 close parentheses squared end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of begin inline style 2 over 2 end style times log presuperscript 3 space open parentheses x minus 1 close parentheses end exponent end cell row blank equals cell open parentheses 3 to the power of begin inline style 1 half end style end exponent close parentheses to the power of begin inline style log presuperscript 3 space open parentheses x minus 1 close parentheses end style end exponent end cell row blank equals cell 3 to the power of begin inline style 1 half end style times begin inline style blank presuperscript 3 end style begin inline style log end style begin inline style space end style begin inline style open parentheses x minus 1 close parentheses end style end exponent end cell row blank equals cell 3 to the power of log presuperscript 3 space open parentheses x minus 1 close parentheses to the power of 1 half end exponent end exponent end cell row blank equals cell begin inline style 3 to the power of log presuperscript 3 space square root of x minus 1 end root end exponent end style begin inline style space end style end cell row blank equals cell begin inline style square root of x minus 1 end root end style end cell end table    

Sehingga, bentuk sederhana dari open parentheses square root of 3 close parentheses to the power of log presuperscript 9 space open parentheses x minus 1 close parentheses squared end exponent adalah square root of x minus 1 end root.

Jadi, jawaban yang tepat adalah D.

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