If $ a = 3,643,712,546,890,623,517 $ and $ b = 179,563,128 $, determine the number of digits of the product $ a.b $. I went searching the site and found this post where advise to use logarithm Calculate the number of digits in a product of large numbers

But I am looking for something simpler. I did

$ 3.10^{18} <u = 3 ... <3,7.10^{18} $ and $ 10^8 <v = 179 ... <2.10^8 $

$$ 3.10^{26} <u.v <7,4.10^{26} $$ so that's 27 digits. Would this be right? Is there a more specific way to solve?