Jika 8m=46 dan 9n=27, maka nilai (m×n) adalah ...

Pertanyaan

Jika begin mathsize 14px style 8 to the power of m equals 4 to the power of 6 end style dan begin mathsize 14px style 9 to the power of n equals 27 end style, maka nilai begin mathsize 14px style open parentheses m cross times n close parentheses end style adalah ...

  1. begin mathsize 14px style 3 end style 

  2. size 14px 4 size 14px comma size 14px 5 

  3. size 14px 6 

  4. size 14px 9 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Pembahasan

Ingat kembali sifat dan persamaan eksponen berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m cross times n end exponent end cell row cell a to the power of f open parentheses x close parentheses end exponent equals a to the power of p end cell rightwards arrow cell f open parentheses x close parentheses equals p end cell end table

Diketahui begin mathsize 14px style 8 to the power of m equals 4 to the power of 6 end style dan begin mathsize 14px style 9 to the power of n equals 27 end style, akan ditentukan nilai dari begin mathsize 14px style open parentheses m cross times n close parentheses end style.

Terlebih dahulu tentukan nilai m.

table attributes columnalign right center left columnspacing 2px end attributes row cell 8 to the power of m end cell equals cell 4 to the power of 6 end cell row cell open parentheses 2 cubed close parentheses to the power of m end cell equals cell open parentheses 2 squared close parentheses to the power of 6 end cell row cell 2 to the power of 3 cross times m end exponent end cell equals cell 2 to the power of 2 cross times 6 end exponent end cell row cell 2 to the power of 3 m end exponent end cell equals cell 2 to the power of 12 end cell row cell 3 m end cell equals 12 row m equals 4 end table

Kemudian tentukan nilai n.

table attributes columnalign right center left columnspacing 2px end attributes row cell 9 to the power of n end cell equals 27 row cell open parentheses 3 squared close parentheses to the power of n end cell equals cell open parentheses 3 cubed close parentheses end cell row cell 3 to the power of 2 cross times n end exponent end cell equals cell 3 cubed end cell row cell 3 to the power of 2 n end exponent end cell equals cell 3 cubed end cell row cell 2 n end cell equals 3 row n equals cell 3 over 2 end cell end table

Karena begin mathsize 14px style m equals 4 space dan space n equals 3 over 2 end style sehingga diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell m cross times n end cell equals cell open parentheses 4 close parentheses cross times open parentheses 3 over 2 close parentheses end cell row blank equals cell 12 over 2 end cell row blank equals 6 end table

Oleh karena itu, jawaban yang tepat adalah C.

141

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