Googol is equal to $10^{100}$. To determine the number of bits that it needs to represented in binary, we need to rewrite Googol with a base of $2$. This is the correct answer:
$$10^{100} = 2^{\frac{100}{\log2}}$$
Can someone show me the process work for getting to that answer?
Edit: Please don't use the answer in your solution. Simply go from $10^{100}$ to the answer, assuming you had never known the answer in the first place.
We want to solve for $x$, where: $$ 10^{100} = 2^x $$
To this end, we take the common logarithm of both sides to obtain: \begin{align*} \log(10^{100}) &= \log(2^x) \\ 100\log(10) &= x\log(2) \\ 100 &= x\log(2) \\ x &= \frac{100}{\log 2} \end{align*}
Hence, we conclude that: $$ 10^{100} = 2^{\frac{100}{\log 2}} $$