Question
Solve :$4^{x - 2}- 2^{x + 1}= 0$
✓
Answer
$4^{x - 2}- 2^{x + 1}= 0$
$\Rightarrow 4^{x - 2}= 2^{x + 1}$
$\Rightarrow (2^2)^{x - 2}= 2^{x + 1}$
$\Rightarrow (2^2)^{x - 4}= 2^{x + 1}$
We know that if bases are equal, the powers are equal
$\Rightarrow 2x - 4 = x + 1$
$\Rightarrow 2x - x = 4 + 1$
$\Rightarrow x = 5.$
$\Rightarrow 4^{x - 2}= 2^{x + 1}$
$\Rightarrow (2^2)^{x - 2}= 2^{x + 1}$
$\Rightarrow (2^2)^{x - 4}= 2^{x + 1}$
We know that if bases are equal, the powers are equal
$\Rightarrow 2x - 4 = x + 1$
$\Rightarrow 2x - x = 4 + 1$
$\Rightarrow x = 5.$
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