Using the properties of logarithms, we can simplify the given equation:

log(7;X) = log(7;2.5) + 4*log(7;2) - log(7;10)

Since log(a;b) + log(a;c) = log(a;b*c), we can combine the second and third terms:

log(7;X) = log(7;2.5) + log(7;2^4) - log(7;10)

Now, we simplify further:

log(7;X) = log(7;2.5*2^4) - log(7;10)

log(7;X) = log(7;2.5*16) - log(7;10)
log(7;X) = log(7;40) - log(7;10)

Using the property log(a;b) - log(a;c) = log(a;b/c), we can further simplify:

log(7;X) = log(7;40/10)
log(7;X) = log(7;4)

Therefore, X = 4.