nt.number theory - Transcendence of $log 2$

I am not number theorist, forgive me if this is a stupid question.

Recently I was curious about the ideas behind the transcendence of $log 2$.

For the number $e$, It seems that the transcendence can be obtained by a argument of fast convergence of the Taylor expansion but the same ideas do not apply to $log 2$. Talking with number theorists I got an explanation based on the results of Baker. Unfortunately this person can not point me towards a survey or a paper discussing the ideas behind this transcendence so I come here to ask:

What are the ideas behind the transcendence of this number?

Any text (paper,book, blog) suitable for non number theorists is also welcome as an answer.