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 .

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 straight n equals 2 over 3.

Pembahasan

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.

83

0.0 (0 rating)

Iklan

Pertanyaan serupa

Jika ( 3 p ) 2 − ( 2 p ) 2 ( 3 p 2 ) 2 + ( 4 p 2 ) 2 ​ = 80 , nilai dari p 2 = ....

375

5.0

Jawaban terverifikasi

Iklan

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia