December, 2018

Ask Uncle Colin: A Mess of Logs

Dear Uncle Colin, I have to show that $-\frac{x}{2} = \ln (\sqrt{1+e^x} – \sqrt{e^x }) + \ln (\sqrt{1+e^{-x}} + 1)$. I can’t get it anywhere near the right form! – Proof Of It Not Coming – Any Reasonable Explanation? Hi, POINCARE, and thanks for your message! That’s a bit of

Exchange rates on board

“Three teas, please,” said the passenger ahead of me in the queue. The Armorique was due in Plymouth any minute, and tea was of the essence. “That’s £4.65, or €5.601.” Hang on a moment, I thought, remembering to order my own tea as well. 560 isn’t a multiple of 3.