Hi, so this gets me nowhere, especially after I get rid of the logarithm and I get 5^{7/2}. Maybe I'm missing something and you can point it out, this is what I have:

log_{5}x + (log_{5}125/log_{5}x) = 7/2

log_{5}x(125 - x) = 7/2

log_{5}(125x - x^{2}) = 7/2

125x - x^{2}= 5^{7/2 }125x - x^{2}= 279.5

x^{2}- 125x - 279.5 = 0

Trial and error is no good, and quadratic seems to be the only option.

Thanks