minta tolong kak, sama caranya
Sifat Logaritma
[tex]{}^{a} \log {b} + {}^{a} \log {c} = {}^{a} \log {(b \times c)} [/tex]
[tex] {}^{a} \log {b} - {}^{a} \log {c} = {}^{a} \log {\frac{b}{c}} \\[/tex]
[tex]{}^{a^{n}} \log {b^{m}} = \frac{m}{n} \times {}^{a} \log {b}\\[/tex]
[tex]{}^{a} \log {a} = 1[/tex]
[tex]\\[/tex]
[tex] {}^{3} \log 9 + {}^{3} \log 108 - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log (9 \times 108) - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log 972 - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log \frac{972}{4} + {}^{9} \log 27 \\ = {}^{3} \log 243 + {}^{9} \log 27 \\ = {}^{3} \log {3}^{5} + {}^{ {3}^{2} } \log {3}^{3} \\ = (5 \times {}^{3} \log 3) + ( \frac{3}{2} \times {}^{3} \log 3) \\ = (5 \times 1) + ( \frac{3}{2} \times 1) \\ = 5 + \frac{3}{2} \\ = \frac{10}{2} + \frac{3}{2} \\ = \frac{13}{2} [/tex]
[tex]\\[/tex]
atau
[tex]\\[/tex]
[tex] {}^{3} \log 9 + {}^{3} \log 108 - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log 9 + {}^{3} \log (27 \times 4) - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log 9 + {}^{3} \log 27 + {}^{3} \log 4 - {}^{3} \log 4 + {}^{9} \log 27 \\ = {}^{3} \log 9 + {}^{3} \log 27+ {}^{9} \log 27 \\ = {}^{3} \log 3^{2} + {}^{3} \log 3^{3} + {}^{9} \log 27 \\ = {}^{3} \log (3^{2} \times 3^{3}) + {}^{9} \log 27 \\ = {}^{3} \log {3}^{5} + {}^{ {3}^{2} } \log {3}^{3} \\ = (5 \times {}^{3} \log 3) + ( \frac{3}{2} \times {}^{3} \log 3) \\ = (5 \times 1) + ( \frac{3}{2} \times 1) \\ = 5 + \frac{3}{2} \\ = \frac{10}{2} + \frac{3}{2} \\ = \frac{13}{2} [/tex]
Semoga membantu.
Jawab:
Penjelasan dengan langkah-langkah:
[tex]^{3}\log9+^{3}\log108-^{3}\log4+^{9}\log27\\ \\^{3}\log(\frac{9\times108}{4})+^{3^2}\log3^3\\ \\^{3}\log243+\frac{3}{2}.^{3}\log3\\ \\^{3}\log3^5+\frac{3}{2}.^{3}\log3\\ \\5.^{3}\log3+\frac{3}{2}.^{3}\log3\\ \\5+\frac{3}{2}\\ \\\frac{13}{2}[/tex]
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