We are given that log(x+1) (x^2+3x-14)=2.

We know that log(a) b = c => b = c^a

log(x+1) (x^2+3x-14)=2

=> x^2 + 3x - 14 = (x + 1)^2

=> x^2 + 3x - 14 = x^2 + 1 + 2x

=> x = 15

**The required value of x is 15.**

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