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Question

What values of x satisfy the following inequality :
log2(log3(4x+1))>log2(log3(2x+3)) ?

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Solution

Since the base is 2, which is greater than 1, the given inequality implies log3(4x+1)>log3(2x+3).
This further implies that 4x+1>2x+3, or 2x>2x>1.
Therefore, x must be greater than 1.
In addition, the arguments of all the logarithms must be positive, but this is indeed the case when x is greater than 1.
Therefore, the solution set is x>1.

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