Answer:
3/8
Explanation:
In terms of powers of 4, we have ...
(4^-1)^(3z -1) = (4^2)^(z+2)×(4^3)^(z-2)
Taking logarithms base 4*, we have ...
-(3z -1) = 2(z +2) +3(z -2)
-3z +1 = 5z -2 . . . . simplify
3 = 8z . . . . . . . . . . add 3z+2
z = 3/8 . . . . . . . . . .divide by 8
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* This is equivalent to equating exponents of the same base. You're making use of the rules of exponents ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
1/a = a^-1
and the logarithm relations ...
logb(b^x) = x
log(xy) = log(x) +log(y)