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Hitunglah begin mathsize 14px style log presuperscript 3 1 over 9 square root of 3 equals space... end style 

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style log presuperscript 3 1 over 9 square root of 3 equals negative 3 over 2 end style.

Pembahasan

Logaritma adalah suatu operasi invers atau kebalikan dari perpangkatan.

Terdapat dua sifat logaritma yang digunakan dalam proses penyelesaian, yaitu:

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

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 1 over 9 square root of 3 end cell equals cell log presuperscript 3 square root of 1 over 9 squared cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 1 over 3 to the power of 4 cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 4 end exponent cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 3 end exponent end root end cell row blank equals cell log presuperscript 3 space open parentheses 3 to the power of negative 3 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row blank equals cell log presuperscript 3 space 3 to the power of negative begin inline style 3 over 2 end style end exponent end cell row blank equals cell negative 3 over 2 cross times log presuperscript 3 space 3 end cell row blank equals cell negative 3 over 2 end cell end table end style 

Jadi, nilai begin mathsize 14px style log presuperscript 3 1 over 9 square root of 3 equals negative 3 over 2 end style.

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