Solve `2^(2x) - 3 (2^(x+1)) + 8` = 0please show step by step and any websites that could help me

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`2^(2x) - 3(2^(x+1))+ 8 = 0`

`2^(2x) -3(2^x 2^1) + 8= 0`

`2^(2x) -6(2^x)+ 8= 0`

`(2^x)^2 -6(2^x)+8= 0`

`==> t= 2^x`

`==> t^2 - 6t + 8= 0`

`==> (t-4)(t-2)= 0`

`==> t= 4 ==> 2^x = 4 ==> x = 2`

`==> t= 2==> 2^x =2 ==> x = 1`

`==> x = {1,2}`

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