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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.