3)
The given output values are
a*b^x
a*b^(x + 1)
a*b^(x + 2)
The ratio of the second output to the first output is
a*b^(x + 1) / a*b^x
a cancels out. Thus, we have
b^(x + 1)/b^x
Recall the law of exponents which states that
a^b/a^c = a^(b - c)
Thus,
b^(x + 1)/b^x = b^(x + 1 - x) = b^1
b^(x + 1)/b^x = b
Thus,
a*b^(x + 1) / a*b^x = b
Again, the ratio of the third output to the second output is
a*b^(x + 2) / a*b^(x + 1)
a cancels out. Thus, we have
b^(x + 2)/b^(x + 1)
By appying the same law of exponents, we have
b^(x + 2- (x + 1)
= b^(x + 2 - x - 1)
= b^(x - x + 2 - 1)
= b^1
Thus,
b^(x + 2)/b^(x + 1) = b
Thus, the constant ratio is b