A Proof for Prime Numbers

Question

Show that among k-digit numbers, one in about every 2.3k is a prime.

How can we prove this question? Thanks.

Answer 1

$10^k\le x < 10^{k+1}\implies \ln 10^k\le \ln x < \ln 10^{k+1}\implies$ $k\ln 10\le\ln x<(k+1)\ln 10$, where $ln 10\approx2,3$.

Answer 2

Try using the prime number theorem! :)