solve-8-x-2-x-6-x-3-x-2-find-x-

Question Number 171730 by Mikenice last updated on 20/Jun/22

s o l v e \frac{8^{x} - 2^{x}}{6^{x} - 3^{x}} = 2 . f i n d x

Answered by puissant last updated on 20/Jun/22

\frac{8^{x} - 2^{x}}{6^{x} - 3^{x}} = 2 \Rightarrow \frac{2^{3 x} - 2^{x}}{2^{x} . 3^{x} - 3^{x}} = 2

\Rightarrow \frac{2^{x} (2^{x} - 1) (2^{x} + 1)}{3^{x} (2^{x} - 1)} = 2

2^{x} - 1 \neq 0, x \neq 0

\Rightarrow \frac{2^{x} (2^{x} + 1)}{3^{x}} = 2

\Rightarrow 2^{x - 1} (2^{x} + 1) = 3^{x}

∙ f o r x ⩾ 2, n o s o l u t i o n .

∙ f o r x = 1, 2^{1 - 1} (2^{1} + 1) = 3 = 3^{1} .

∙ f o r x ⩽ - 1, n o s o l u t i o n .

S = {1} .

\dots \dots \dots . L e p u i s s a n t \dots \dots \dots .

Commented by Mikenice last updated on 20/Jun/22

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