The given expression (1P03)4 represents a number in base 4, where P is an unknown digit. We can expand this expression in terms of powers of 4 to obtain its value in base 10:

(1P03)4 = 1 4^3 + P 4^2 + 0 4^1 + 3 4^0

= 64 + 16P + 3

We are given that this expression is equal to 11510, so we can solve for P:

64 + 16P + 3 = 115

16P = 115 - 64 - 3

16P = 48

P = 48/16

P = 3

So the value of P is 3.