How many digits?

Number of digits of a number n is equals (log n) +1.

$log 2^{9998654}$ $\times$ $7^{81359421}$ $\times$ $3^{28467}$ $+1$
$=log 2^{9998654} + log 7^{81359421} + log 3^{28467} +1$
$=9998654 \times log 2 + 81359421 \times log 7 + 28467 \times log 3 +1$
we know $log 2=.301029995, log 3 = .477121254, log 7 = .84509804$

So the result is,
$\boxed{71780165}$

Yes, as Farhabi Mojib mentioned, the number of digits of a number $n$ is given by: $f_d(n) = \lfloor \log{n} \rfloor + 1$ , where $\lfloor \space \rfloor$ is the greatest integer function. Therefore,

$f_d(2^{9998654}\times 7^{81359421}\times 3^{28467})$

$= \lfloor 9998654\log{2} + 81359421\log{7} + 28467\log{3} \rfloor + 1$

$= \lfloor 9998654\times 0.301029996 + 81359421\times 0.84509804$ $\quad + 28467\times 0.477121255 \rfloor + 1$

$= \lfloor 3009894.77 + 68756687.22 + 13582.21076 \rfloor + 1$

$= \lfloor 71780164.2 \rfloor + 1 = \boxed {71780165}$