What is the inverse of log base 2 of 16x?

Let Y=log2(16X)

Inverse fuctions means swapping the X and Y, and rearranging to make Y the subject of the formula.

Hence: X=log2(16Y)

2^X=16Y

(rules of logs, called the Base,Answer,Power rule sometimes)

Dividing both sides by 16 to make y the subject

Y=2^X/16

16 can be rewritten as 2^4

Hence, Y=2^X/2^4

Laws of indices. Writing as one base to a single exponent. As the bases are same we can minus the exponents

Y=2^(X-4)

log base 2 * 16x= y

log base 2*16y=x

2 to the power of x= 16y

2^x/16= y

:)