sifat logaritma bagian 2​

roycewalshulv – March 14, 2023

sifat logaritma bagian 2​

Jawaban:

1. 5

2. 1

3. -3/4

4. 5 1/4

Penjelasan dengan langkah-langkah:

1.

[tex] {4}^{ {}^{2} log(3) } - {3}^{ {}^{9} log(16) } \\ = {2}^{2( {}^{2} log(3)) } - {3}^{ \frac{2}{2} \times {}^{3} log(4) } \\ = {2}^{ {}^{2} log( {3}^{2} ) } - {3}^{ {}^{3} log(4) } \\ = {3}^{2} - 4 \\ = 9 - 4\\ = 5[/tex]

2.

[tex] {}^{9} log(144) - 2. {}^{3} log(2) \\ = {}^{ {3}^{2} } log( {12}^{2} ) - { }^{3} log( {2}^{2} ) \\ = \frac{2}{2} \times {}^{3} log(12) - {}^{3} log(4) \\ = {}^{3} log(12) - {}^{3} log(4) \\ = {}^{3} log(12 \div 4) \\ = {}^{3} log(3) \\ = 1[/tex]

3.

[tex] {}^{3} log( \frac{1}{8} ) \times {}^{4} log( \sqrt{3} ) \\ = {}^{3} log( {2}^{ - 3} ) \times {}^{ {2}^{2} } log( {3}^{ \frac{1}{2} } ) \\ = - 3 \times {}^{3} log(2) \times {}^{2} log(3) \times \frac{ \frac{1}{2} }{2} \\ = - 3 \times 1 \times \frac{1}{4} \\ = - \frac{3}{4} [/tex]

4.

[tex] \frac{ {}^{16} log(8) + {}^{3} log(8) \times {}^{2} log( \frac{1}{9} ) }{ {}^{5} log(2) - {}^{5} log(10) } \\ = \frac{ {}^{16} log(8) + {}^{3} log( {2}^{3} ) \times {}^{2} log( {3}^{ - 2} ) }{ {}^{5} log(2 \div 10) } \\ = \frac{ {}^{ {2}^{4} } log( {2}^{3} ) + 3 \times {}^{3} log(2) \times {}^{2} log(3) \times - 2 }{ {}^{5} log( \frac{1}{5} ) } \\ = \frac{ \frac{3}{4} + 3 \times ( - 2) }{ {}^{5} log( {5}^{ - 1} ) } \\ = \frac{ \frac{3}{4} - 6 }{ - 1} \\ = \frac{ - 5 \frac{1}{4} }{ - 1} \\ = 5 \frac{1}{4} [/tex]

Terima kasih juga untuk latihan soalnya.