Question

2^2x - 3 × 2^x × 4 + 32 = 0 solve to find 'x'

Answer 1

Answer

The value of x is 3 and 2

Given

The equation is :

$\sf \bullet \: \: 2 {}^{2x} - 3 \times 2 {}^{x} \times 4 + 32 = 0$

Solution

$\sf Let \: us \: consider \: 2 {}^{x} \: be \: \: k \: so \: that \\ \sf the \: equation \: becomes :$

$\sf \dashrightarrow {k}^{2} - 3 \times k \times 4 + 32 = 0 \\ \\ \sf\dashrightarrow {k}^{2} - 12k + 32 = 0 \\ \\ \sf\dashrightarrow {k}^{2} - 4k - 8k + 32 = 0 \\ \\ \sf\dashrightarrow k(k - 4) - 8(k - 4) = 0 \\ \\ \sf \dashrightarrow (k - 8)(k - 4) = 0$

Thus we have ,

$\sf \longrightarrow{k} - 8 = 0 \: \: and \: \longrightarrow{k - 4 = 0} \\ \\ \sf\longrightarrow k = 8 \: \: and \: \longrightarrow k = 4 \\ \\ \sf\longrightarrow 2 {}^{x} = 2 {}^{3} \: \: and \: \longrightarrow2 {}^{x} = {2}^{2} \\ \\ \sf\longrightarrow x = 3 \: \: and \: \: \longrightarrow x = 2$

Answer 2

Step-by-step explanation:

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