To Log or Not to Log

We can find the number of digits in a number by taking the floor of a log of a number, and adding one, as such: $\lfloor logx\rfloor+1=$ number of digits in $x$ . Therefore, we have the number of digits in $5^x=\lfloor xlog5 \rfloor+1$ , because of the property $log_xy^z=zlog_xy$ . $log5=log10-log2$ , because of the property $logx-logy=log\frac{x}{y}$ , and from there it is just brute force by calculating out each scenario for $x>50$ .