Pertanyaan

Tentukan Nilai dari: ( 3 lo g 27 ) − 2 × 2 lo g 8 6 + 5 lo g 1 10 5 lo g 25 1 × [ 3 − 1 lo g 9 5 − 2 lo g 3 ⋅ 3 lo g 32 1 ]

Tentukan Nilai dari:

$\frac{^{5} lo g \frac{1}{25} \times [ ^{3^{- 1}} lo g 9 ^{5} - ^{2} lo g 3 \cdot ^{3} lo g \frac{1}{32} ]}{( ^{3} lo g 27 ) ^{- 2} \times ^{2} lo g 8 ^{6} + ^{5} lo g 1 ^{10}}$

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

diperoleh hasil .

diperoleh hasil $begin mathsize 14px style fraction numerator log presuperscript 5 space begin display style 1 over 25 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction equals negative 15 end style$ .

Pembahasan

Gunakan sifat logaritma berikut: Perhatikan perhitungan berikut: Jadi, diperoleh hasil .

Gunakan sifat logaritma berikut:

Perhatikan perhitungan berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell fraction numerator log presuperscript 5 space begin display style 1 over 25 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction end cell row blank equals cell fraction numerator log presuperscript 5 space begin display style 5 squared end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space open parentheses 3 squared close parentheses to the power of 5 minus log presuperscript 2 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 3 cubed close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space open parentheses 2 cubed close parentheses to the power of 6 plus 10 space log presuperscript 5 space 1 end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 5 space begin display style 5 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 3 to the power of 10 minus log presuperscript 2 space begin display style 2 to the power of 5 end style close square brackets over denominator open parentheses 3 space log presuperscript 3 space 3 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 2 to the power of 18 plus 10 space open parentheses 0 close parentheses end fraction end cell row blank equals cell fraction numerator 2 space open parentheses 1 close parentheses open square brackets begin display style fraction numerator 10 over denominator negative 1 end fraction end style log presuperscript 3 space 3 minus 5 space log presuperscript 2 space begin display style 2 end style close square brackets over denominator open parentheses 3 space open parentheses 1 close parentheses close parentheses to the power of negative 2 end exponent cross times 18 space log presuperscript 2 space 2 plus 0 end fraction end cell row blank equals cell fraction numerator 2 space open square brackets negative 10 space open parentheses 1 close parentheses minus 5 space open parentheses 1 close parentheses close square brackets over denominator 3 to the power of negative 2 end exponent cross times 18 space open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open square brackets negative 10 minus 5 close square brackets over denominator begin display style 1 over 3 squared end style cross times 18 end fraction end cell row blank equals cell fraction numerator 2 open square brackets negative 15 close square brackets over denominator begin display style 1 over 9 end style cross times 18 end fraction end cell row blank equals cell fraction numerator negative 30 over denominator 2 end fraction end cell row blank equals cell negative 15 end cell end table end style$

Jadi, diperoleh hasil $begin mathsize 14px style fraction numerator log presuperscript 5 space begin display style 1 over 25 end style open square brackets log presuperscript 3 to the power of negative 1 end exponent end presuperscript space 9 to the power of 5 minus log presuperscript 2 space 3 times log presuperscript 3 space begin display style 1 over 32 end style close square brackets over denominator open parentheses log presuperscript 3 space 27 close parentheses to the power of negative 2 end exponent cross times log presuperscript 2 space 8 to the power of 6 plus log presuperscript 5 space 1 to the power of 10 end fraction equals negative 15 end style$ .