2log(7)32-log(7)256-2log(7)14

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To simplify this expression, we can use the property of logarithms that states:

log(a) + log(b) = log(a * b)

Therefore, we can rewrite the expression as:

2log(7)32 - log(7)256 - 2log(7)14 = log(7)(32^2) - log(7)256 - log(7)(14^2)

= log(7)(1024) - log(7)256 - log(7)(196)

= log(7)(1024 / 256) - log(7)196

= log(7)4 - log(7)196

Now, using another property of logarithms which states:

log(a) - log(b) = log(a / b)

we can simplify the expression further:

log(7)4 - log(7)196 = log(7)(4 / 196)

= log(7)(1 / 49)

= log(7)(7^-2)

= -2

Therefore, the simplified expression is -2.