Question

Solve the equation
$3( 2^{x}+1) - 2^{x + 2} + 5 = 0$

Answer 1

$Answer: \\ \\ Now, \\ \\ 3( 2^{x}+1) - 2^{x + 2} + 5 = 0 \\ \\ = > 3( {2}^{x} + 1) - {2}^{2} {2}^{x} + 5 = 0 \\ \\ = > 3( {2}^{x} + 1) - 4( {2}^{x} ) + 5 = 0 \\ \\ = > 3(y + 1 )- 4y + 5 = 0, \\ assuming \: \: {2}^{x} = y \\ \\ = > 3y + 3 - 4y + 5 = 0 \\ \\ = > y = 8 \\ \\ = > {2}^{x} = 8 \\ \\ = > {2}^{x} = {2}^{3} \\ \\ Comparing \: \: both \: \: sides, \: \: we \: \: get \\ \\ x = 3$

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