First, we'll use the negative power property of
exponentials:
1/11^(-x-10) =
11^-(-x-10)
Now, we'll re-write the
equation:
11^(5x-6) =
11^-(-x-10)
Since the bases are matching, we'll use one to
one property:
5x - 6 = x +
10
We'll isolate x to the left side. For this reason,
we'll subtract x both sides:
5x - x - 6 =
10
We'll combine like terms and we'll add 6 both
sides:
4x = 10 + 6
4x =
16
We'll divide by 4:
x =
4
The solution of the equation is x =
4.
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