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pochemuha
2 years ago
9

"2^{4x + 14} = {64}^{x + 2} " alt="2^{4x + 14} = {64}^{x + 2} " align="absmiddle" class="latex-formula">
helpppppppppppppppp​
Mathematics
2 answers:
frutty [35]2 years ago
8 0

\\ \rm\longmapsto 2^{4x+4}=64^{x+2}

\\ \rm\longmapsto 2^{4x+4}=(2^6)^{x+2}

\\ \rm\longmapsto 2^{4x+4}=2^{6(x+2)}

\\ \rm\longmapsto 4x+4=6(x+2)

\\ \rm\longmapsto 4x+4=6x+12

\\ \rm\longmapsto 4-12=6x-4x

\\ \rm\longmapsto -8=2x

\\ \rm\longmapsto x=\dfrac{-8}{2}

\\ \rm\longmapsto x=-4

stepladder [879]2 years ago
8 0

Answer:

x = 1

Step-by-step explanation:

{2}^{4x + 14}  =  {64}^{x + 2}

➡️ {2}^{4x + 14}  = ( {2}^{6}  {)}^{x + 2}

➡️ {2}^{4x + 14}  =  {2}^{6x + 12}

➡️ 4x + 14 = 6x + 12

➡️ 14 - 12 = 6x - 4x

➡️ 2x = 2

➡️ x = 1

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