Where can I find a modern (preferably elementary) proof of Tchebychef's 1852 theorem that the prime counting function $\pi(x)$ has order of magnitude $x/\log(x)$. Perferrably with the original bounds as outlined in the first two pages of this survey article of prof. D. Goldfeld. I will also count as modern Tchebychef's original approach coated in modern notation and terminology. Basically I only require this so that I am most likely to understand it as well as possible, not because of a particular dislike for Tchebychef's method itself, which I think is very cool from the outlines provided in the mentioned paper. I speak nor read French very well.
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1P.L. Tchebychef, M ́ emoire sur les nombres premiers, J. de Math. Pures Appl. (1) 17 (1852), 366–390; reprinted in Oeuvres 1 (1899), 49–70. – Will Jagy Aug 28 '17 at 17:57
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And adapt this answer – reuns Aug 29 '17 at 08:55