Question

Solve 2 to power x+1 + 2 to power x+ 2 =192​

Answer 1

${\cal{{2}^{x+1} + {2}^{x+2} = 192}}$

${\cal{({2}^{x})({2}^{1}) + ({2}^{x})({2}^{2}) = 192}}$

${\cal{({2}^{x})(2) + ({2}^{x})(4) = 192}}$

${\cal{(6)({2}^{x})} = 192}$

${\cal{{2}^{x} = {\cancel{\dfrac{192}{6}}}}}$

${\cal{{2}^{x} = 32}}$

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∴ $\Large{\underline{\underline{\red{\cal{x = 5}}}}}$.. .. .. $\qquad$( ∵ ${2}^{5} = 32$ )

Answer 2

$\large{\blue {2}^{ \blue{x + 1}}} + { \large{ \blue {2}^{ \blue{x + 2}}}} = { \large{ \blue{192}}}$

$( {2}^{x} )( {2}^{x} ) + ( {2}^{x})( {2}^{2}) = 192$

$( {2}^{x})( {2}) + ( {2}^{x})(2 \times 2 = 4) = 192$

$(4 + 2) + ( {2}^{x} + {2}^{x})$

$(6)( {2}^{x}) = 192$

$\large {2}^{x} = \frac{ \cancel192}{ \cancel6}$

${2}^{x} ={32}$$x = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( {2}^{5} = 32)$

$\red{ \boxed{Hope \: it's \: helps \: uhh :) }}$