1) To solve the equation log4(3x+1) = 2, we can rewrite it in exponential form:
4^2 = 3x + 1
16 = 3x + 1
3x = 15
x = 5

2) For the equation log1.6(3x - 16) = log1.6(x - 4), we can rewrite it in exponential form:
1.6^(3x - 16) = 1.6^(x - 4)
3x - 16 = x - 4
2x = 12
x = 6

3) Lastly, for the equation log14(4x - 10) = log14(3x - 8), we can rewrite it in exponential form:
14^(4x - 10) = 14^(3x - 8)
4x - 10 = 3x - 8
x = 2

Therefore, the solutions to the three logarithmic equations are x = 5, x = 6, and x = 2.