First, we can simplify each of the logarithms individually:

[tex]\log_6{90} = \log_6{6 \times 15} = \log_6{6} + \log_6{15} = 1 + \log_6{15}[/tex]

[tex]\log_6{2,5} = \log_6{\frac{5}{2}} = -\log_6{2} - \log_6{5} = -1 - \log_6{5}[/tex]

[tex]\log_4{16} = 2[/tex] since [tex]4^2 = 16[/tex]

Now, substituting these back into the original expression:

[tex]1 + \log_6{15} - (-1 - \log_6{5}) + \log_4{16} = 2 + \log_6{15} + 1 + \log_6{5} + 2 = 5 + \log_6{15} + \log_6{5}[/tex]

So the simplified expression is [tex]5 + \log_6{15} + \log_6{5}[/tex].