To solve the inequalities, we first need to convert them into exponential form and then solve for x.

1) Log2(x-3) < 1
This can be rewritten as:
2^(log2(x-3)) < 2^1
x-3 < 2
x < 5

Therefore, the solution to the first inequality is x < 5.

2) Log8(5x-3) < 2
This can be rewritten as:
8^(log8(5x-3)) < 8^2
5x-3 < 64
5x < 67
x < 67/5

Therefore, the solution to the second inequality is x < 67/5.

In conclusion, the solutions to the given inequalities are x < 5 and x < 67/5.