Suppose that f(x) and g(x) are functions which satisfy f(g(x))=x^2 and g(f(x))=x^3 for all x ≥ 1. If g(16)=16, then compute log_2 of g(4).

I'm not quite sure what to do here.

To compute log₂ of g(4), we need to find the value of g(4) first.

Given that g(16) = 16, and using the second equation g(f(x)) = x³ for all x ≥ 1, we can substitute f(x) = 16:

g( f(x) ) = x³
g( 16 ) = x³
16 = x³

To find x, we take the cube root of both sides:

∛(16) = ∛(x³)
2 = x

Now that we know x = 2, we can substitute it into the first equation f(g(x)) = x²:

f( g(x) ) = x²
f( g(4) ) = 2²
f( g(4) ) = 4

We have f( g(4) ) = 4.

Since g(4) = y, we can rewrite the equation as:

f(y) = 4

Now, we need to solve for y. However, there is not enough information given to determine the exact value of y.

Therefore, we cannot compute the log₂ of g(4) with the provided information.