Pertanyaan

Hasil dari adalah ....

Hasil dari $begin mathsize 14px style fraction numerator log presuperscript 6 space 27 times log presuperscript square root of 3 end presuperscript space 36 minus log presuperscript 4 space begin display style 1 over 64 end style over denominator log presuperscript 6 space 36 minus log presuperscript 6 space 6 square root of 6 end fraction end style$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

Hasil dari adalah 30 .

Hasil dari $\frac{{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{27}\boldsymbol\cdot{}^\sqrt{\mathbf3}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{36}\boldsymbol-{}^{\mathbf4}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{\displaystyle\frac1{64}}}{{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{36}\boldsymbol-{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf6\sqrt{\mathbf6}}$ adalah

30

Pembahasan

Ingat kembali sifat-sifat logaritma: Maka: Jadi, Hasil dari adalah 30 .

Ingat kembali sifat-sifat logaritma:

Maka:

$fraction numerator log presuperscript 6 space 27 times log presuperscript square root of 3 end presuperscript space 36 minus log presuperscript 4 space begin display style 1 over 64 end style over denominator log presuperscript 6 space 36 minus log presuperscript 6 space 6 square root of 6 end fraction equals fraction numerator log presuperscript 6 space 3 cubed times log presuperscript 3 to the power of begin display style 1 half end style end exponent end presuperscript space 6 squared minus log presuperscript 2 squared end presuperscript space begin display style 2 to the power of negative 6 end exponent end style over denominator log presuperscript 6 space 6 squared minus log presuperscript 6 space 6 times 6 to the power of begin display style 1 half end style end exponent end fraction equals fraction numerator 3 times log presuperscript 6 space 3 times begin display style fraction numerator 2 over denominator begin display style 1 half end style end fraction end style log presuperscript 3 space 6 minus open parentheses begin display style fraction numerator negative 6 over denominator 2 end fraction end style close parentheses times log presuperscript 2 space begin display style 2 end style over denominator log presuperscript 6 space 6 squared minus log presuperscript 6 space 6 to the power of begin display style 3 over 2 end style end exponent end fraction equals fraction numerator 3 times 4 times log presuperscript 6 space 3 times log presuperscript 3 space 6 plus 3 times 1 over denominator log presuperscript 6 space begin display style 6 squared over 6 to the power of begin display style 3 over 2 end style end exponent end style end fraction equals fraction numerator 12 times log presuperscript 6 space 6 plus 3 over denominator log presuperscript 6 space 6 to the power of begin display style 1 half end style end exponent end fraction equals fraction numerator 12 times 1 plus 3 over denominator begin display style 1 half end style times log presuperscript 6 space 6 end fraction equals fraction numerator 12 plus 3 over denominator begin display style 1 half end style times 1 end fraction equals fraction numerator 15 over denominator begin display style 1 half end style end fraction equals 30$

Jadi, Hasil dari $\frac{{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{27}\boldsymbol\cdot{}^\sqrt{\mathbf3}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{36}\boldsymbol-{}^{\mathbf4}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{\displaystyle\frac1{64}}}{{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf{36}\boldsymbol-{}^{\mathbf6}\mathbf l\mathbf o\mathbf g\boldsymbol\;\mathbf6\sqrt{\mathbf6}}$ adalah $30$ .