Question

$\huge \green{\rm {8}^{x} + {4}^{x} + {2}^{x} = 14}$​

Answer 1

${8}^{x} + {4}^{x} + {2}^{x} = 14 \\ {2}^{x} (4 + 2 + 1) = 14 \\ {2}^{x} = \frac{14}{7} \\ {2}^{x} = {2}^{1} \\ x = 1$

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Answer 2

Answer:

The solution is $x=1$

Step-by-step explanation:

Given equation is

     $8^x+4^x+2^x=14$

  $\Rightarrow (2^x)^3+(2^x)^2+(2^x)=14$

Substitute $2^x=t$

     $\Rightarrow t^3+t^2+t-14=0\\\Rightarrow (t-2)(t^2+3t+7)=0$

Clearly, the second factor does not have real root

    $\Rightarrow t-2=0\Rightarrow t=2$

       $\Rightarrow 2^x=2\Rightarrow 2^x=2^1\Rightarrow x=1$