Please solve and check?

Question

a)5^2n+1 = 1 / 125

b)1 / 256 = 2^2-5w

c)3^x-1 = 1 / 81

d) 6^3x-7 = 1 / 6

Thank you

Answer 1

identify each of the numbers as a power and equate the power

125 = 5^-3
2n+1 = -3
2n = -4
n = -2

1/256 = 2^-8
2-5w = -8
5w =10
w = 2

81 = 3^4
x-1 = 4
x = 5

3x-7 = -1
3x = 6
x = 2