Question

please solve guys as fast as you can plzzzzzzz
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Answer 1

Step-by-step explanation:

We have,

$log( {x}^{3} + 5 ) = 3 log(x + 2)$

$= > log( {x}^{3} + 5) = log(x + 2) ^{3}$

$= > {x}^{3} + 5 = {(x + 2)}^{3}$

$= > {x}^{3} + 5 = {x}^{3} + 3. {x}^{2} .2 + 3.x.(2)^{2} + {2}^{3}$

$= > 5 = 6 {x}^{2} + 12x + 8$

$= > 6 {x}^{2} + 12x + 3 = 0$

$= > 2 {x}^{2} + 4x + 1 = 0$

$= > x = \frac{ - 4 + \sqrt{ {4}^{2} - 4 \times 2 \times 1} }{2 \times 2}\: \: or \: \: x = \frac{ - 4 - \sqrt{ {4}^{2} - 4 \times 2 \times 1} }{2 \times 2}$

$= > x = \frac{ - 4 + \sqrt{ 8} }{4} \: \: or \: \: x = \frac{ - 4 - \sqrt{ 8} }{4}$

$= > x = \frac{ - 4 + 2 \sqrt{ 2} }{4} \: \: or \: \: x = \frac{ - 4 - 2\sqrt{ 2} }{4}$

$= > x = \frac{ - 2+ \sqrt{ 2} }{2} \: \: or \: \: x = \frac{ - 2 - \sqrt{ 2} }{2}$