Logs, 2s, and 3s

Algebra Level 2

Find all real solutions xx to

3log⁡2(x)−1=log⁡2(32x−1).3\log_2(x) - 1 = \log_2\left(\frac32 x-1\right).

Enter your answer as the sum of all such x x .

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Patrick Corn by Patrick Corn
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