how can you use 2 to the power of 1 to 10 to find out what 2 to the power of 40 is?

I don't understand what you mean isi?

I am not sure what anon wants either.

Maybe

$$2^{40}=2^{10}*2^{10}*2^{10}*2^{10}$$

$${{\mathtt{2}}}^{{\mathtt{10}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{10}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{10}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{10}}} = {\mathtt{1\,099\,511\,627\,776}}$$

$${log}_{10}\left({\mathtt{2}}\right) = {\mathtt{0.301\: \!029\: \!995\: \!663\: \!981\: \!2}}$$

$${log}_{10}\left({{\mathtt{2}}}^{{\mathtt{40}}}\right) = {\mathtt{12.041\: \!199\: \!826\: \!559\: \!248}}$$

There is a relationship of 4.