Dear Dirichlet, Issue 01

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the Prof’s help? Send your problems to

Dear Dirichlet,

This week’s problem sheet asks me to show that $\log(x) < x-1$ for all $x > 0$. To me this seems obviously true – a quick sketch backs it up as well. I think I’m supposed to use Taylor series or something but I’m not sure where to start. Can you help?

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