Nilai dari 2 log akar 27.3 log 1/625.5log akar 1/32

Mata Pelajaran : Matematika Peminatan
Kelas : 10
Bab : 02 - Fungsi Logaritma



[tex] {}^{2} log( \sqrt{27} ) \times {}^{3} log( \frac{1}{625} ) \times {}^{5} log( \sqrt{ \frac{1}{32} } ) \\ = {}^{2} log(3 {}^{ \frac{3}{2} } ). {}^{3} log(5 {}^{ - 4} ) . {}^{5} log( \sqrt{ \frac{1}{32} } ) \\ = \frac{3}{2} \times {}^{2} log(3 ) \times ( - 4. {}^{3} log5) \times {}^{5} log(2 {}^{ - \frac{5}{2} } ) \\ = \frac{3}{2} \times {}^{2} log(3) \times ( - 4. {}^{3} log5) \times ( - \frac{5}{2} \times {}^{5} log2) \\ = 3. {}^{2} log(3) \times 2. {}^{3} log(5) \times \frac{5}{2} \times {}^{5} log(2) \\ = 3. {}^{2} log(3) . {}^{3} log(5) \times 5. {}^{5} log(2) \\ = 3 \times \frac{ {}^{5} log(3) }{ {}^{5} log(2) } \times {}^{3} log(5) \times 5. {}^{5} log(2) \\ = 3. {}^{5} log(3) . {}^{3} log(5) \times 5 \\ = 3 \times 1 \times 5 \\ = 15[/tex]