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Jika x merupakan penyelesaian dari , maka nilai dari  adalah ...

Pertanyaan

Jika x merupakan penyelesaian dari 3 to the power of 3 x minus 1 end exponent equals 9 to the power of x, maka nilai dari 3 x plus 9 adalah ...

  1. 3

  2. 6

  3. 8

  4. 12

Pembahasan Soal:

3 to the power of 3 x minus 1 end exponent equals 9 to the power of x 3 to the power of 3 x minus 1 end exponent equals 3 to the power of 2 x end exponent


Karena bilangan pokoknya sudah sama, maka tinggal menyamakan bilangan pangkatnya.


table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 1 end cell equals cell 2 x end cell row x equals 1 end table


table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 9 end cell equals cell 3 times 1 plus 9 end cell row blank equals 12 end table


Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 11 Juli 2021

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Pertanyaan yang serupa

Himpunan penyelesaian dari persamaan eksponen  adalah ...

Pembahasan Soal:

3 to the power of x cubed minus 10 x squared minus 11 x minus 3 end exponent equals square root of 1 over 729 end root  3 to the power of x cubed minus 10 x squared minus 11 x minus 3 end exponent equals open parentheses 3 to the power of negative 6 end exponent close parentheses to the power of 1 half end exponent  3 to the power of x cubed minus 10 x squared minus 11 x minus 3 end exponent equals 3 to the power of negative 3 end exponent  x cubed minus 10 x squared minus 11 x minus 3 equals negative 3  x cubed minus 10 x squared minus 11 x equals 0  x left parenthesis x squared minus 10 x minus 11 right parenthesis equals 0  x equals 0 space logical or space x equals 11 space logical or space x equals negative 1

HP= [-1,0,11)

0

Roboguru

Nilai  yang memenuhi persamaan   adalah ...

Pembahasan Soal:

Ingat kembali:

  • Jika a to the power of f open parentheses x close parentheses end exponent equals a to the power of g open parentheses x close parentheses end exponent dengan a>0,a=1 maka f open parentheses x close parentheses equals g open parentheses x close parentheses
  • a to the power of m a to the power of n equals a to the power of m plus n end exponent, dengan a>0,a=1
  • open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent, dengan a>0,a=1

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 6 over 7 times 3 to the power of 3 straight x minus 1 end exponent plus 27 to the power of straight x over 21 equals 1 close parentheses di space kali space 21 end cell row cell 3 times 6 times 3 to the power of 3 x minus 1 end exponent plus open parentheses 3 cubed close parentheses to the power of x end cell equals 21 row cell 6 times 3 to the power of 1 plus 3 x minus 1 end exponent plus open parentheses 3 close parentheses to the power of 3 x end exponent end cell equals 21 row cell 6 times 3 to the power of 3 x end exponent plus 3 to the power of 3 x end exponent end cell equals 21 row cell 7 times 3 to the power of 3 x end exponent end cell equals 21 row cell 3 to the power of 3 x end exponent end cell equals cell 21 over 7 end cell row cell 3 to the power of 3 x end exponent end cell equals 3 row cell 3 to the power of 3 x end exponent end cell equals cell 3 to the power of 1 end cell row blank blank blank end table    

karena a=3, bearti a>0,a=1 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x end cell equals 1 row x equals cell 1 third end cell end table  

Jadi, Nilai x yang memenuhi persamaan 6 over 7 times 3 to the power of 3 x minus 1 end exponent plus 27 to the power of x over 21 equals 1  adalah 1 third.

Oleh karena itu, jawaban yang benar adalah C.space 

0

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 27 to the power of 2 over 3 end exponent plus 16 to the power of 3 over 2 end exponent close parentheses to the power of 1 half end exponent end cell equals cell open parentheses open parentheses 3 cubed close parentheses to the power of 2 over 3 end exponent plus open parentheses 4 squared close parentheses to the power of 3 over 2 end exponent close parentheses to the power of 1 half end exponent end cell row blank equals cell open parentheses 3 squared plus 4 cubed close parentheses to the power of 1 half end exponent end cell row blank equals cell left parenthesis 9 plus 64 right parenthesis to the power of 1 half end exponent end cell row blank equals cell square root of 73 end cell row blank almost equal to cell 8 comma 544 end cell end table end style

Dengan demikian, diperoleh hasil begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 27 to the power of 2 over 3 end exponent plus 16 to the power of 3 over 2 end exponent close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 1 half end exponent end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 73 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank almost equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 544 end table end style.

Jadi, tidak ada jawaban yang tepat.

0

Roboguru

Himpunan penyelesaian persamaan  adalah ...

Pembahasan Soal:

Persamaan 2.9 to the power of x minus 3 to the power of x plus 1 end exponent plus 1 equals 0, misalkan 3 to the power of x equals a

table attributes columnalign right center left columnspacing 0px end attributes row cell 2.9 to the power of x minus 3 to the power of x plus 1 end exponent plus 1 end cell equals 0 row cell 2. left parenthesis 3 squared right parenthesis to the power of x minus 3 to the power of x plus 1 end exponent plus 1 end cell equals 0 row cell 2.3 to the power of 2 x end exponent minus 3 to the power of x plus 1 end exponent plus 1 end cell equals 0 row cell 2 a squared minus 3 to the power of x times 3 to the power of 1 plus 1 end cell equals 0 row cell 2 a squared minus a times 3 plus 1 end cell equals 0 row cell 2 a squared minus 3 a plus 1 end cell equals 0 row cell left parenthesis 2 a minus 1 right parenthesis left parenthesis a minus 1 right parenthesis end cell equals 0 row cell 2 a minus 1 end cell equals 0 row cell 2 a end cell equals 1 row a equals cell 1 half end cell row cell a minus 1 end cell equals 0 row a equals 1 row cell 3 to the power of x end cell equals cell 1 half end cell row x equals cell log presuperscript 3 1 half end cell row blank blank blank row cell 3 to the power of x end cell equals 1 row cell 3 to the power of 0 end cell equals 1 row x equals 0 row blank blank blank row HP equals cell open curly brackets 0 comma space log presuperscript 3 1 half close curly brackets end cell row blank blank blank end table

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Bentuk sederhana dari adalah ....

Pembahasan Soal:

begin mathsize 14px style open parentheses fraction numerator 4 a to the power of negative 2 end exponent b squared c over denominator 12 a to the power of negative 5 end exponent b to the power of 4 c to the power of negative 1 end exponent end fraction close parentheses to the power of negative 1 end exponent equals open parentheses fraction numerator a to the power of negative 2 minus left parenthesis negative 5 right parenthesis end exponent b to the power of 2 minus 4 end exponent c to the power of 1 minus open parentheses negative 1 close parentheses end exponent over denominator 3 end fraction close parentheses to the power of negative 1 end exponent  equals open parentheses fraction numerator a cubed b to the power of negative 2 end exponent c squared over denominator 3 end fraction close parentheses to the power of negative 1 end exponent  equals fraction numerator a to the power of negative 3 end exponent b squared c to the power of negative 2 end exponent over denominator 3 to the power of negative 1 end exponent end fraction  equals fraction numerator 3 b squared over denominator a cubed c squared end fraction end style

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