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 colin@flyingcoloursmaths.co.uk 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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