To solve this logarithmic equation, we can use the properties of logarithms to condense the equation into a single logarithm.

First, we can use the change of base formula to convert the logarithms into a common base.

log16 (x) = log (x) / log (16)
log4 (x) = log (x) / log (4)
log2 (x) = log (x) / log (2)

So, the equation becomes:

log (x) / log (16) + log (x) / log (4) + log (x) / log (2) = 7

Now, we can combine the logarithms using the properties of logarithms:

log (x) [1/log(16) + 1/log(4) + 1/log(2)] = 7

Simplify the expression inside the brackets:

log (x) [1/4 + 1/2 + 1] = 7
log (x) [1/4 + 2/4 + 4/4] = 7
log (x) [7/4] = 7

Now, we can solve for x by exponentiating both sides:

x = 10^(7/4)
x = 10^(1.75)
x ≈ 56.23

Therefore, the solution to the equation log16 (x) + log4 (x) + log2 (x) = 7 is approximately x = 56.23.