- #1
Helly123
- 581
- 20
Homework Statement
$$\log_2 \sqrt{2x-1} < \log_4 x$$
Homework Equations
The Attempt at a Solution
$$\log_2 \sqrt{2x-1} < \log_4 x$$
$$\log_2 {2x-1}^{1/2} < \log_2 \sqrt{x}$$
$$1/2 \log_2 {(2x-1)} - \log_2 \sqrt{x} < 0$$
$$ 1/2 \log_2 {\frac{(2x-1)}{ x}} < 0$$
$$ -1/2 \log_2 {(2x-1) x} < 0$$
$$ 1/2 \log_2 {(2x^2-x)} > 0$$
$$ \log_2 {\sqrt{(2x^2-x)}} >\log_2 {1} $$
$$2x^2 - x > 1$$
$$2x^2 - x - 1 = 0$$
$$(2x + 1)(x -1) = 0$$
$$x < -1/2 \ \ or \ \ x > 1$$
but I get wrong answers. How to find the right answer? can you help me?
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