To solve this equation, we need to find the value of k that makes both sides equal.
We can start by rewriting the logarithmic expression using the logarithmic properties:
log16^k + 4^(k+1) = 1/4^3
k * log16 + (k+1) * log4 = -3 * log4
k * log16 + k * log4 + log4 = -3 * log4
k * (log16 + log4) + log4 = -3 * log4
k * log64 + log4 = -3 * log4
k * 6 + 1 = -9
k = -2
Therefore, the value of k that satisfies the equation is k = -2.