Calculations using googolplexes How can I calculate $\dfrac{10^{10^{100 }}}{ 10^{10^{70}}}$?
I have tried using logs ie:
$$\frac{10^{10^{100}}}{10^{10^{70}}}$$
$$=\frac{(100\times \ln(10)) \times \ln(10)}{(70\times \ln(10)) \times \ln(10)}$$
$$=\frac{10}{7}$$
which looks incorrect as $\dfrac{10^{10}}{10^7}=1000$
What am I doing wrong?

$$\frac{10^{10^{100}}}{10^{10^{70}}}=10^{10^{100}-10^{70}}=10^{10^{70}(10^{30}-1)}$$
There's more you can do but it doesn't really get any simpler than that. It's $1$ with $10^{70}(10^{30}-1)$ zeros after it. You can turn the $10^{30}-1$ into a string of 30 nines, but I don't see any particular purpose to that. You should read the exponent as "way too many zeros to write down."
