We know that loga x = y, then x = ay
Therefore, on comparing with the given equation we get log7 ( x^2 - x + 37 ) = 2^1 = 2 and furthermore from this we can say that x^2 - x + 37 = 7^2 = 49
x^2 - x +37 - 49 = 0
x^2 - x - 12 = 0
on solving the given equation we get x = 4 or x = -3
The value that satisfies the given answer-choices is x = 4.