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  4. The value of x satisfying the equation 22 x-8 ⋅ 2x=-12, is

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Q. The value of x satisfying the equation
$2^{2 x}-8 \cdot 2^x=-12$, is

Continuity and Differentiability

Solution:

$ 2^{ x }= t $
$t ^2-8 t +12=0$
$( t -6)( t -2)=0 $
$2^{ x }=6 \Rightarrow x =\log _2 6=1+\frac{\log 3}{\log 2} \Rightarrow (A)$
$2^{ x }=2 \Rightarrow x =1 \Rightarrow (D)$