Question

`2^(4x + 14) = {64}^(x + 2)`
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Answer 1

x = 1

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`

Answer 2

`\\ \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=(-8)/(2)`

`\\ \rm\longmapsto x=-4`