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Diketahui 7 ( 8 p ) = 9 ( 5 q ) dan 7 ( 1 6 p + 1 ) = 12 ( 5 q ) .Buktikan bahwa 2 p = 12 1 ​

Diketahui  .  Buktikan bahwa  

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N. Puspita

Master Teacher

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dari uraian yang teah dipaparkan di atas, persamaan merupakan persamaan yang benar.

dari uraian yang teah dipaparkan di atas, persamaan 2 to the power of p equals 1 over 12 merupakan persamaan yang benar. 

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Diketahui . Ingat! Sifat bilangan berpangkat: Maka: Bagi persamaan (1) dengan persamaan (2), maka: Jadi, dari uraian yang teah dipaparkan di atas, persamaan merupakan persamaan yang benar.

Diketahui 7 open parentheses 8 to the power of p close parentheses equals 9 open parentheses 5 to the power of q close parentheses space dan space 7 open parentheses 16 to the power of p plus 1 end exponent close parentheses equals 12 open parentheses 5 to the power of q close parentheses . 

Ingat!

Sifat bilangan berpangkat:

  • a to the power of m space colon space a to the power of n equals a to the power of m minus n end exponent 
  • open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent 
  • a to the power of negative n end exponent equals 1 over a to the power of n  

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 7 open parentheses 8 to the power of p close parentheses end cell equals cell 9 open parentheses 5 to the power of q close parentheses end cell row cell 7 open parentheses 2 cubed close parentheses to the power of p end cell equals cell 9 open parentheses 5 to the power of q close parentheses end cell row cell 7 open parentheses 2 to the power of 3 p end exponent close parentheses end cell equals cell 9 open parentheses 5 to the power of q close parentheses space.... space left parenthesis 1 right parenthesis end cell end table   

table attributes columnalign right center left columnspacing 0px end attributes row cell 7 open parentheses 16 to the power of p plus 1 end exponent close parentheses end cell equals cell 12 open parentheses 5 to the power of q close parentheses end cell row cell 7 left parenthesis 16 to the power of p.16 to the power of 1 right parenthesis end cell equals cell 12 open parentheses 5 to the power of q close parentheses end cell row cell 112 left parenthesis 16 to the power of p right parenthesis end cell equals cell 12 open parentheses 5 to the power of q close parentheses end cell row cell 112 open parentheses 2 to the power of 4 close parentheses to the power of p end cell equals cell 12 open parentheses 5 to the power of q close parentheses end cell row cell 112 open parentheses 2 to the power of 4 p end exponent close parentheses end cell equals cell 12 open parentheses 5 to the power of q close parentheses space.... space left parenthesis 2 right parenthesis end cell end table 

Bagi persamaan (1) dengan persamaan (2), maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 7 open parentheses 2 to the power of 3 p end exponent close parentheses over denominator 112 open parentheses 2 to the power of 4 p end exponent close parentheses end fraction end cell equals cell fraction numerator 9 up diagonal strike open parentheses 5 to the power of q close parentheses end strike space over denominator 12 up diagonal strike open parentheses 5 to the power of q close parentheses end strike space end fraction end cell row cell fraction numerator up diagonal strike 7 open parentheses 2 to the power of 3 p end exponent close parentheses over denominator 16 cross times up diagonal strike 7 open parentheses 2 to the power of 4 p end exponent close parentheses end fraction end cell equals cell 9 over 12 end cell row cell 2 to the power of 3 p end exponent over 2 to the power of 4 p end exponent end cell equals cell 9 over 12 cross times 16 end cell row cell 2 to the power of 3 p minus 4 p end exponent end cell equals cell 144 over 12 end cell row cell 2 to the power of negative p end exponent end cell equals 12 row cell 1 over 2 to the power of p end cell equals 12 row cell 1 over 12 end cell equals cell 2 to the power of p space left parenthesis terbukti right parenthesis end cell end table 

Jadi, dari uraian yang teah dipaparkan di atas, persamaan 2 to the power of p equals 1 over 12 merupakan persamaan yang benar. 

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