Express 4 In 2 - In 4 as a single natural logarithm. In 2 In 4 In 64

Mathematics

1 answer:

Stella [2.4K]3 years ago

6 0

Answer : In 4

Explanation: edg

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BlackZzzverrR [31]

1. $\frac{ 5( {4x}^{3} {y}^{2} ) ^{3}}{( {4x}^{5} {y}^{3}) ^{4} } \\ = \frac{5 \times {4}^{3} \times {x}^{3 \times 3} \times {y}^{2 \times 3} }{ {4}^{4} \times {x}^{5 \times 4} \times {y}^{3 \times 4} } \\ = \frac{5 \times 64 \times {x}^{9} \times {y}^{6} }{256 \times {x}^{20} \times {y}^{12} } \\ = \frac{320 {x}^{9} {y}^{6} }{256 {x}^{20} {y}^{12} } \\ = \frac{5 {x}^{9 - 20} {y}^{6 - 12} }{4} \\ = \frac{5}{4 {x}^{11} {y}^{6} }$

2. ${3}^{5x - 4} = {9}^{2x + 12} \\ = > {3}^{5x - 4} = {3}^{2(2x + 12)} \\ = > {3}^{5x - 4} = {3}^{4x + 24} \\ = > 5x - 4 = 4x + 24 \\ = > 5x - 4x = 24 + 4 \\ = > x = 28$