Question

$2^{4x + 14} = {64}^{x + 2}$
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Answer 1

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

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

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

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

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

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

$\\ \rm\longmapsto -8=2x$

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

$\\ \rm\longmapsto x=-4$

Answer 2

Answer:

x = 1

Step-by-step explanation:

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

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

➡️ ${2}^{4x + 14} = {2}^{6x + 12}$

➡️ $4x + 14 = 6x + 12$

➡️ $14 - 12 = 6x - 4x$

➡️ $2x = 2$

➡️ $x = 1$