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Jika 7log 3=a dan 3log 4=b, tentukan nilai logaritma berikut. a. 3log 186

Pertanyaan

Jika log presuperscript 7 space 3 equals a dan log presuperscript 3 space 4 equals b, tentukan nilai logaritma berikut.

a. log presuperscript 3 space 186

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jika diasumsikan soalnya adalah log presuperscript 3 space 196 hasilnya adalah fraction numerator a b plus 2 over denominator a end fraction.

Pembahasan

Ingat sifat bentuk logaritma:

table attributes columnalign right center left columnspacing 0px end attributes 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 comma space c not equal to 1 end cell row cell log presuperscript a space a end cell equals 1 row cell log presuperscript a space b c end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b to the power of m end cell equals cell m times log presuperscript a space b end cell end table 

Diketahui log presuperscript 3 space 4 equals b maka jika diuraikan:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space 4 end cell equals b row cell log presuperscript 3 space 2 squared end cell equals b row cell 2 times log presuperscript 3 space 2 end cell equals b row cell log presuperscript 3 space 2 end cell equals cell b over 2 end cell end table 

sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space 186 end cell equals cell fraction numerator log presuperscript 3 space 186 over denominator log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space open parentheses 6 cross times 31 close parentheses over denominator 1 end fraction end cell row blank equals cell log presuperscript 3 space 6 plus log presuperscript 3 space 31 end cell row blank equals cell scriptbase log space open parentheses 2 cross times 3 close parentheses plus log presuperscript 3 space 31 end scriptbase presuperscript 3 end cell row blank equals cell scriptbase log space 2 plus end scriptbase presuperscript 3 scriptbase log space 3 plus log presuperscript 3 space 31 end scriptbase presuperscript 3 end cell row blank equals cell b over 2 plus 1 plus log presuperscript 3 space 31 end cell end table 

Dengan demikian nilai dari log presuperscript 3 space 186 adalah b over 2 plus 1 plus log presuperscript 3 space 31.

 

Diasumsikan misalkan soalnya adalah log presuperscript 3 space 196.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space 186 end cell equals cell fraction numerator log presuperscript 3 space 196 over denominator log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space open parentheses 4 cross times 7 squared close parentheses over denominator 1 end fraction end cell row blank equals cell log presuperscript 3 space 4 plus log presuperscript 3 space 7 squared end cell row blank equals cell b plus 2 times 1 over a end cell row blank equals cell b plus 2 over a end cell row blank equals cell fraction numerator a b plus 2 over denominator a end fraction end cell end table 

Dengan demikian jika diasumsikan soalnya adalah log presuperscript 3 space 196 hasilnya adalah fraction numerator a b plus 2 over denominator a end fraction.

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