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Question

What values of x satisfy the following inequality ?
log1/2(3x)>log1/2(2x+3) ?

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Solution

Since the base is 12, which is less than 1, the given inequality implies 3x<2x+3. Then, x<3.
Additionally, the argument of each logarithm must be positive, so 3x>0 and 2x+3>0.
The former is more restrictive, so the solution set is 0<x<3.

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