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Pertanyaan

Diketahui sistem persamaan { 4 x + 5 y = 6 4 y x ​ = 5 ​ Nilai x 1 ​ + y 1 ​ = ....

Diketahui sistem persamaan

 

Nilai  

  1. log subscript 3 space 4 

  2. log subscript 3 space 20 

  3. log subscript 3 space 5 

  4. log subscript 3 space 25 

  5. log subscript 3 space 6 

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

. jawaban yang tepat adalah C.

. jawaban yang tepat adalah C.

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Pembahasan

Diketahui: Ditanya: Jawab: Persamaan Eksponen dengan basis berupa bilangan. sifat-sifat eksponen Persamaan logaritma dengan basis dan numerus berbeda. sifat -sifat logaritma Jadi, nilai adalah Jadi. jawaban yang tepat adalah C.

Diketahui:

open curly brackets table attributes columnalign left end attributes row cell 4 to the power of x plus 5 to the power of y equals 6 end cell row cell 4 to the power of x over y end exponent equals 5 end cell end table close

Ditanya:

1 over x plus 1 over y equals

Jawab:

Persamaan Eksponen dengan basis berupa bilangan.

sifat-sifat eksponen

a to the power of p times a to the power of q equals a to the power of p plus q end exponent a to the power of p divided by a to the power of q equals a to the power of p minus q end exponent open parentheses a to the power of p close parentheses to the power of q equals a to the power of p times q end exponent

Persamaan logaritma dengan basis dan numerus berbeda.

sifat -sifat logaritma 

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a open parentheses b times c close parentheses end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a open parentheses b over c close parentheses end cell equals cell log presuperscript a space b minus log presuperscript a space c end cell row cell log presuperscript a to the power of m end presuperscript space b to the power of n end cell equals cell n over m times log presuperscript a space b end cell row cell log presuperscript a space b end cell equals cell fraction numerator log presuperscript c space b over denominator log presuperscript c space a end fraction equals fraction numerator 1 over denominator log presuperscript b space a end fraction end cell end table 

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets table attributes columnalign left end attributes row cell 4 to the power of x plus 5 to the power of y equals 6 space.... asterisk times 1 end cell row cell 4 to the power of x over y end exponent equals 5 space.... asterisk times 2 end cell end table close end cell row cell open parentheses 4 to the power of x over y end exponent close parentheses to the power of y end cell equals cell 5 to the power of y end cell row cell 4 to the power of x end cell equals cell 5 to the power of y end cell row blank blank cell s u b s t i t u s i space p a d a space p e r s space asterisk times 1 end cell row cell 4 to the power of x plus 5 to the power of y end cell equals 6 row cell 5 to the power of y plus 5 to the power of y end cell equals 6 row cell 2 times 5 to the power of y end cell equals 6 row cell 5 to the power of y end cell equals 3 row cell log space 5 to the power of y end cell equals cell log space 3 end cell row cell y times log space 5 end cell equals cell log space 3 end cell row y equals cell fraction numerator log space 3 over denominator log space 5 end fraction end cell row cell 1 over y end cell equals cell fraction numerator log space 5 over denominator log space 3 end fraction equals log presuperscript 3 space 5 end cell row cell 4 to the power of x end cell equals 3 row cell log space 4 to the power of x end cell equals cell log space 3 end cell row cell x space log space 4 end cell equals cell log space 3 end cell row x equals cell fraction numerator log space 3 over denominator log space 4 end fraction end cell row cell 1 over x end cell equals cell fraction numerator log space 4 over denominator log space 3 end fraction equals scriptbase log space 4 end scriptbase presuperscript 3 end cell end table

 

1 over x plus 1 over y equals log presuperscript 3 space 4 plus scriptbase log space 5 equals log presuperscript 3 space 4 times 5 equals log presuperscript 3 space 20 end scriptbase presuperscript 3 

Jadi, nilai  1 over x plus 1 over y adalah log presuperscript 3 space 20 

Jadi. jawaban yang tepat adalah C.

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