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Hasil dari begin mathsize 14px style fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction... end style.

Pembahasan Soal:

Gunakan sifat logaritma berikut:

begin mathsize 14px style log presuperscript a space a equals 1 log presuperscript a space b to the power of n equals n space log presuperscript a space b log presuperscript a to the power of m end presuperscript space b to the power of n equals n over m space log presuperscript a space b log presuperscript a space b times log presuperscript b space c equals log presuperscript a space c end style 

Perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction end cell equals cell fraction numerator log presuperscript 3 space 6 squared times log presuperscript 6 space 81 plus log presuperscript 2 squared end presuperscript space 2 to the power of 5 over denominator log presuperscript begin display style 3 to the power of negative 2 end exponent end style end presuperscript space 3 cubed end fraction end cell row blank equals cell fraction numerator 2 log presuperscript 3 space 6 times log presuperscript 6 space 81 plus begin display style 5 over 2 end style space open parentheses 1 close parentheses over denominator begin display style fraction numerator 3 over denominator negative 2 end fraction end style space open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 3 space 81 plus begin display style 5 over 2 end style over denominator begin display style negative 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 3 space 3 to the power of 4 plus 5 over 2 over denominator begin display style negative 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 2 cross times 4 space log presuperscript 3 space 3 plus begin display style 5 over 2 end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 8 plus begin display style 5 over 2 end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 16 plus 5 over denominator 2 end fraction end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell 21 over 2 cross times open parentheses negative 2 over 3 close parentheses end cell row cell fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction end cell equals cell negative 7 end cell end table end style

Jadi, diperoleh begin mathsize 14px style fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction equals negative 7 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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