Question

${2}^{x + 1} = \: {4}^{x - 3} \: find \: the \: value \: of \: x$
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Answer 1

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$\overbrace{ \underbrace{ \fcolorbox{white}{pink}{ \blue\dag \tt Answer :– x = 4 \red\dag}}}$

$\tt \longrightarrow \: {2}^{x + 1} = \: {4}^{x - 3} \\ \\ \longrightarrow \tt 2 ^{x + 1} = {2}^{(2 \times x) - 3} \: \: \\ \\ \longrightarrow \tt \: x + 1 = 2x - 3 \: \\ \\ \longrightarrow \tt \: x - 2x = - 3 - 1 \\ \\ \longrightarrow \tt - x = - 4 \:\\ \\ \rm So, therefore \rm \boxed{ \tt\red{{x = 4}}}$

Important in this solution -

• $\tt [ \red{As \: we \: know, \: when \: base \: is \: same \: then \: we \: equate \: the \: powers }]$

• $[ \: ( - ) \times ( - ) = ( + ) ]$

• $[ \red{ As \: we \: know,{2}^{2} = 4 }]$

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