Question

Find the total number of digits in 8^232*25^348

Answer 1

Well, the answer is the integer immediately after (or the integer itself if it is) the logarithm of this number to the base 10.

We may represent it as,

$\lceil\log{8^{232}\times25^{348}}\rceil$

So,

$\begin{aligned}\implies\ \ &\lceil\log(8^{232}\times25^{348})\rceil\\\\\implies\ \ &\lceil\log((2^3)^{232}\times(5^2)^{348})\rceil\\\\\implies\ \ &\lceil\log(2^{696}\times5^{696})\rceil\\\\\implies\ \ &\lceil\log((2\times5)^{696})\rceil\\\\\implies\ \ &\lceil696\log(2\times5)\rceil\end{aligned}$

$\begin{aligned}\implies\ \ &\lceil696\log10\rceil\\\\\implies\ \ &\mathbf{696}\end{aligned}$

Hence 696 is the answer.