Pertanyaan

Tentukan nilai m dan n yang memenuhi 2 7 2 m 3 2 m × 8 3 n − 1 = 3 2 × 2 3 .

Tentukan nilai m dan n yang memenuhi $\frac{3 ^{2 m} \times 8 ^{3 n - 1}}{2 7 ^{2 m}} = 3^{2} \times 2^{3}$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai m dan n yang memenuhi persamaan adalah dan .

nilai m dan n yang memenuhi persamaan $fraction numerator 3 to the power of 2 straight m end exponent 8 to the power of 3 straight n minus 1 end exponent over denominator 27 to the power of 2 straight m end exponent end fraction equals 3 squared cross times 2 cubed$ adalah straight m equals negative 1 half

dan

Pembahasan

Ingatlah sifat bilangan berpangkat berikut: Berdasarkan sifat di atas, maka: Pada hasil persamaan di atas, bilangan pokoknya sudah sama sehingga: dan Dengan demikian, nilai m dan n yang memenuhi persamaan adalah dan .

Ingatlah sifat bilangan berpangkat berikut:

left parenthesis straight i right parenthesis space straight a to the power of straight m over straight a to the power of straight n equals straight a to the power of straight m minus straight n end exponent left parenthesis ii right parenthesis space open parentheses straight a to the power of straight m close parentheses to the power of straight n equals straight a to the power of mn

Berdasarkan sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 to the power of 2 straight m end exponent cross times 8 to the power of 3 straight n minus 1 end exponent over denominator 27 to the power of 2 straight m end exponent end fraction end cell equals cell 3 squared cross times 2 cubed end cell row cell fraction numerator 3 to the power of 2 straight m end exponent cross times open parentheses 2 cubed close parentheses to the power of 3 straight n minus 1 end exponent over denominator open parentheses 3 cubed close parentheses to the power of 2 straight m end exponent end fraction end cell equals cell 3 squared cross times 2 cubed end cell row cell fraction numerator 3 to the power of 2 straight m end exponent cross times 2 to the power of 9 straight n minus 3 end exponent over denominator 3 to the power of 6 straight m end exponent end fraction end cell equals cell 3 squared cross times 2 cubed end cell row cell 3 to the power of 2 straight m minus 6 straight m end exponent cross times 2 to the power of 9 straight n minus 3 end exponent end cell equals cell 3 squared cross times 2 cubed end cell row cell 3 to the power of negative 4 straight m end exponent cross times 2 to the power of 9 straight n minus 3 end exponent end cell equals cell 3 squared cross times 2 cubed end cell end table$

Pada hasil persamaan di atas, bilangan pokoknya sudah sama sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 4 straight m end cell equals 2 row straight m equals cell negative 2 over 4 end cell row straight m equals cell negative 1 half. end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 straight n minus 3 end cell equals 3 row cell 9 straight n end cell equals cell 3 plus 3 end cell row cell 9 straight n end cell equals 6 row straight n equals cell 6 over 9 end cell row straight n equals cell 2 over 3. end cell end table

Dengan demikian, nilai m dan n yang memenuhi persamaan $fraction numerator 3 to the power of 2 straight m end exponent 8 to the power of 3 straight n minus 1 end exponent over denominator 27 to the power of 2 straight m end exponent end fraction equals 3 squared cross times 2 cubed$ adalah straight m equals negative 1 half dan straight n equals 2 over 3 .