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Sum of integral values of x satisfying t...

Sum of integral values of `x` satisfying the inequality `3^((5/2)log_3(12-3x))-3^(log_2(x))>32`

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The correct Answer is:
3
We must have ` 12 - 3x gt 0`
` and x gt 0`
` rArr x in (0, 4)`
Therefore, the integral values are 1, 2, 3.
For ` x = 1 , (3^( 5/2log_(3)9))-(3^(log_(2)1))=3^(5) - 3^(0) gt 32`
Similarly, x = 2 satisfies but not x = 3
Hence, the required sum = 3.
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