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Jika diketahui  dan  maka nilai dari  adalah ...

Pertanyaan

Jika diketahui begin mathsize 14px style log presuperscript 2 space 3 equals a end style dan begin mathsize 14px style log presuperscript 3 space 7 equals b end style maka nilai dari begin mathsize 14px style log presuperscript 24 space 21 end style adalah ...

  1. begin mathsize 14px style fraction numerator a plus a b over denominator 3 plus b end fraction end style 

  2. begin mathsize 14px style fraction numerator a plus 3 b over denominator a plus 3 end fraction end style 

  3. begin mathsize 14px style fraction numerator a plus a b over denominator a plus 3 end fraction end style 

  4. begin mathsize 14px style fraction numerator a plus 3 over denominator a plus a b end fraction end style 

  5. begin mathsize 14px style fraction numerator a plus 3 over denominator a b plus b end fraction end style 

Pembahasan Soal:

Gunakan sifat-sifat logaritma sebagai berikut:

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 p space b over denominator log presuperscript p space a end fraction end cell row cell log presuperscript a space b end cell equals cell fraction numerator 1 over denominator log presuperscript b space a end fraction end cell row cell log presuperscript a space open parentheses b cross 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 space b to the power of m end cell equals cell m times log presuperscript a space b end cell row cell log presuperscript a space a end cell equals 1 end table  

Diketahui undefined maka

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space 3 end cell equals a row cell fraction numerator 1 over denominator log presuperscript 3 space 2 end fraction end cell equals a row cell log presuperscript 3 space 2 end cell equals cell 1 over a end cell end table 

sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space 21 end scriptbase presuperscript 24 end cell equals cell fraction numerator log presuperscript 3 space 21 over denominator log presuperscript 3 space 24 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space open parentheses 7 cross times 3 close parentheses over denominator log presuperscript 3 space open parentheses 8 cross times 3 close parentheses end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator log presuperscript 3 space 8 plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator log presuperscript 3 space 2 cubed plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator log presuperscript 3 space 7 plus log presuperscript 3 space 3 over denominator 3 times log presuperscript 3 space 2 plus log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator b plus 1 over denominator 3 open parentheses begin display style 1 over a end style close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator b plus 1 over denominator begin display style fraction numerator 3 plus a over denominator a end fraction end style end fraction end cell row blank equals cell open parentheses b plus 1 close parentheses cross times fraction numerator a over denominator open parentheses 3 plus a close parentheses end fraction end cell row blank equals cell fraction numerator a plus a b over denominator a plus 3 end fraction end cell end table 

Dengan demikian, nilai dari  begin mathsize 14px style log presuperscript 24 space 21 end style adalah begin mathsize 14px style fraction numerator a plus a b over denominator a plus 3 end fraction end style.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 28 Juli 2021

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