Ask Uncle Colin: Approximating an embedded exponential | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to and Uncle Colin will do what he can.

Dear Uncle Colin,

Help! My calculator is broken and I need to solve – or at least approximate – $0.1 = \frac{x}{e^x – 1}$! How would you do it?

— Every $x$ Produces Outrageous Numbers, Exploring New Techniques

Hi, ExPONENT, and thanks for your message!

That’s a bit of a beast, and you’ll not get an exact solution using elementary…

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