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Pilihlah jawaban a, b, c, d dan e yang menurut anda benar ! Jika  maka ....

Pertanyaan

Pilihlah jawaban a, b, c, d dan e yang menurut anda benar !

Jika begin mathsize 14px style 5 to the power of x equals 4 comma end style maka size 14px 5 to the power of size 14px 1 size 14px minus size 14px 2 size 14px x end exponent size 14px equals....

  1. size 14px 80

  2. size 14px 20 

  3. size 14px 16 over size 14px 3 

  4. size 14px 5 over size 14px 8 

  5. size 14px 5 over size 14px 16 

Pembahasan Soal:

Ingat bahwa:

am÷an(am)n==amnamn

Berdasarkan sifat di atas diperoleh

512x=====51÷52x51÷(52)x5÷(5x)25÷(4)2165

Oleh karena itu, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Eka

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 11 September 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pilihlah jawaban a, b, c, d dan e yang menurut anda benar ! Nilai  yang memenuhi persamaan  adalah….

Pembahasan Soal:

Ingat kembali sifat dan persamaan eksponensial berikut.

anamaf(x)=ac=amnf(x)=c 

Akan ditentukan nilai undefined yang memenuhi persamaan size 14px 3 to the power of size 14px x size 14px minus size 14px 1 end exponent size 14px plus size 14px 3 to the power of size 14px x size 14px equals size 14px 36.

Perhatikan perhitungan berikut.

3x1+3x33x+3x33x+333x343x43x43x3x3x3xx==========3636363636×3108410827333

Diperoleh nilai x=3.

Oleh karena itu, jawaban yang tepat adalah C.

Roboguru

Pembahasan Soal:

Ingat bahwa:

  • n-th root of a to the power of m end root equals a to the power of m over n end exponent comma thin space    thin space a greater or equal than 0 
  • a to the power of m over n end exponent equals open parentheses a to the power of m close parentheses to the power of 1 over n end exponent equals n-th root of a to the power of m end root a to the power of m over n end exponent equals open parentheses a to the power of 1 over n end exponent close parentheses to the power of m equals open parentheses n-th root of a close parentheses to the power of m 
  • a to the power of m times a to the power of n equals a to the power of m plus n end exponent 

Mencari hasil dari akar tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 fourth root of 2 cubed end root times fourth root of 4 cubed end root times 1 over 2 squared fourth root of 2 cubed end root end cell equals cell 2 times 1 over 2 squared times fourth root of 2 cubed end root fourth root of 4 cubed end root fourth root of 2 cubed end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 2 cubed times 4 cubed times 2 cubed end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 4 cubed times 2 to the power of 3 plus 3 end exponent end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 4 cubed times 2 to the power of 6 end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of open parentheses 2 squared close parentheses cubed times 2 to the power of 6 end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 2 to the power of 6 times 2 to the power of 6 end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 2 to the power of 6 plus 6 end exponent end root end cell row blank equals cell 2 times 1 over 2 squared times fourth root of 2 to the power of 12 end root end cell row blank equals cell 2 times 1 over 2 squared times 2 to the power of 12 over 4 end exponent end cell row blank equals cell 2 times 1 over 2 squared times 2 cubed end cell row blank equals cell 2 to the power of 1 plus 3 end exponent over 2 squared end cell row blank equals cell 2 to the power of 4 over 2 squared end cell row blank equals cell 2 squared end cell row blank equals 4 end table  

Jadi, hasil dari 2 fourth root of 2 cubed end root times fourth root of 4 cubed end root times 1 over 2 squared fourth root of 2 cubed end root equals 4.

Dengan demikian, jawaban yang tepat adalah D.

Roboguru

Diketahui , , dan . Nilai  adalah ....

Pembahasan Soal:

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut:

  • a to the power of p over a to the power of q equals a to the power of p minus q end exponent dengan a not equal to 0 
  • a to the power of negative p end exponent equals 1 over a to the power of p dengan a not equal to 0
  • open parentheses a to the power of p close parentheses to the power of q equals a to the power of p q end exponent dengan b not equal to 0

Dengan menggunakan sifat-sifat di atas, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a to the power of negative 2 end exponent b c cubed over denominator a b squared c to the power of negative 1 end exponent end fraction end cell equals cell a to the power of negative 2 end exponent over a to the power of 1 times b to the power of 1 over b squared times c cubed over c to the power of negative 1 end exponent end cell row blank equals cell a to the power of open parentheses negative 2 minus 1 close parentheses end exponent times b to the power of open parentheses 1 minus 2 close parentheses end exponent times c to the power of open parentheses 3 minus open parentheses negative 1 close parentheses close parentheses end exponent end cell row blank equals cell a to the power of negative 3 end exponent b to the power of negative 1 end exponent c to the power of 4 end cell end table 

Substitusi nilai a equals 1 halfb equals 2, dan c equals 1 pada persamaan diatas, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of negative 3 end exponent b to the power of negative 1 end exponent c to the power of 4 end cell equals cell open parentheses 1 half close parentheses to the power of negative 3 end exponent times open parentheses 2 close parentheses to the power of negative 1 end exponent times 1 to the power of 4 end cell row blank equals cell open parentheses 2 to the power of negative 1 end exponent close parentheses to the power of negative 3 end exponent times open parentheses 2 close parentheses to the power of negative 1 end exponent times 1 end cell row blank equals cell 2 cubed times 1 half end cell row blank equals cell 8 times 1 half end cell row blank equals 4 end table 


Dengan demikian, nilai dari fraction numerator a to the power of negative 2 end exponent b c cubed over denominator a b squared c to the power of negative 1 end exponent end fraction equals 4.

Oleh karena itu, jawaban yang benar adalah B.

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Hasil  adalah ....

Pembahasan Soal:

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut:

  • open parentheses a to the power of p close parentheses to the power of q equals a to the power of p cross times q end exponent 
  • open parentheses a b close parentheses to the power of p equals a to the power of p cross times b to the power of p 
  • a to the power of p space colon space a to the power of q equals a to the power of p minus q end exponent dengan a not equal to 0 

Dengan menggunakan sifat-sifat di atas, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses p to the power of 4 q squared close parentheses to the power of 5 space colon space open parentheses p q cubed close parentheses squared end cell equals cell open parentheses p to the power of 4 q squared close parentheses to the power of 5 over open parentheses p q cubed close parentheses squared end cell row blank equals cell fraction numerator open parentheses p to the power of 4 close parentheses to the power of 5 times open parentheses q squared close parentheses to the power of 5 over denominator p squared times open parentheses q cubed close parentheses squared end fraction end cell row blank equals cell fraction numerator p to the power of 4 cross times 5 end exponent times q to the power of 2 cross times 5 end exponent over denominator p squared times q to the power of 3 cross times 2 end exponent end fraction end cell row blank equals cell fraction numerator p to the power of 20 times q to the power of 10 over denominator p squared times q to the power of 6 end fraction end cell row blank equals cell p to the power of 20 minus 2 end exponent times q to the power of 10 minus 6 end exponent end cell row blank equals cell p to the power of 18 q to the power of 4 end cell end table 


Dengan demikian, hasil dari Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Pembahasan Soal:

Ingat bahwa:

  • a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0
  • 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 

Mencari hasil dari akar tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 8 to the power of 3 over 5 end exponent space colon space 8 to the power of 4 over 15 end exponent end cell equals cell 8 to the power of 3 over 5 minus 4 over 15 end exponent end cell row blank equals cell 8 to the power of 9 over 15 minus 4 over 15 end exponent end cell row blank equals cell 8 to the power of 5 over 15 end exponent end cell row blank equals cell 8 to the power of 1 third end exponent end cell row blank equals cell open parentheses 2 cubed close parentheses to the power of 1 third end exponent end cell row blank equals cell 2 to the power of 3 times 1 third end exponent end cell row blank equals 2 end table 

Jadi, hasil dari 8 to the power of 3 over 5 end exponent colon 8 to the power of 4 over 15 end exponent equals 2.

Dengan demikian, jawaban yang tepat adalah B.

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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