Question

Log(25-x3)-3Log (4-x)=0

Answer 1

Explicación paso a paso:

$log(25 - {x}^{3} ) - 3 log((4 - x) = 0 \\ log((25 - {x}^{3} ) - log(( {4 - x})^{3} ) = 0 \\ log( \frac{(25 - {x}^{3}) }{(4 - {x})^{3} } ) = 0 \\ \frac{25 - {x}^{3} }{( {4 - x)}^{3} } = {10}^{0} \\ \frac{25 - {x}^{3} }{( {4 - x)}^{3} } = 1 \\ 25 - {x}^{3} = ( {4 - x)}^{3} \\ 25 - {x}^{3} = 64 - 3( {4)}^{2} x + 3(4)( {x}^{2)} - {x}^{3} \\ 25 - {x}^{3} = 64 - 3(16)x + 12 {x}^{2} - {x}^{3} \\ 25 - {x}^{3} = 64 - 48x + 12 {x}^{2} - {x}^{3} \\ 25 - {x}^{3} - 64 + 48x - 12 {x}^{2} + {x}^{3} = 0 \\ - 39 + 48x - 12 {x}^{2} = 0 \\ - 12 {x}^{2} + 48x - 39 = 0 \\ 12 {x}^{2} - 48x + 39 = 0 \\ 4 {x}^{2} - 16x + 13 = 0 \\ x = \frac{ - b + - \sqrt{ { {b}^{2} - 4ac} } }{2a} \\ x = \frac{ - ( - 16) + - \sqrt{ {( - 16})^{2} - 4(4)(13)} }{2 \times 4} \\ x = \frac{16 + - \sqrt{256 - 208} }{8} \\ x = \frac{16 + - \sqrt{48} }{8} \\ x = \frac{16 + - 4 \sqrt{3} }{8} \\ x = \frac{4(4 - + \sqrt{3)} }{8} \\ x = \frac{4 - + \sqrt{3} }{2} \\ x 1= \frac{4 + \sqrt{3} }{2} \\ x2 = \frac{4 - \sqrt{3} }{2}$