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Question
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
Solution
`2^(2x)-2^(x+3)+2^4=0`
`rArr(2^x)^2-(2^xxx2^3)+(2^2)^2=0`
`rArr(2^x)^2-2xx2^xxx2^2+(2^2)^2=0`
`rArr(2^x-2^2)^2=0`
⇒ 2x - 22 = 0
⇒ 2x = 22
⇒ x = 2
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