Browsing category logarithms

Logarithmic inequalities, and why I always used to get them wrong

A student asks: When I do inequalities with geometric series, I sometimes get my inequality sign the wrong way round - I can usually fudge it, but I'd like to be getting it right. OK, I confess, that student is me, circa 1995. And, in fact, I only figured it

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A reader asks: How does the circle of fifths work?

A fifth - in musical terms - is really three-halves, and if you go through twelve fifths, you end up seven octaves higher. Wait, I'm starting all wrong. A musical note has a frequency - the number of times the sound wave it produces vibrates each second. Middle C, for

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Logarithms revision quiz

You know the drill by now: answer some questions, see if you know your stuff. Just five questions this week.

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A litany of errors, or James Bloody Grime’s Blasted Logarithms Revisited

Problems worthy of attack/ Prove their worth by fighting back - Anon, often quoted by Erdos. A few weeks ago, James bloody Grime posted a question on logarithms that I had a creditable stab at answering. My first answer, it turned out, was wrong. I corrected it, and wrote up

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James Bloody Grime and his blasted logarithms

It's typical of James Grime to ask a really interesting question just as I'm going to bed. I was going to sleep like a log, but suddenly I was awake liking logarithms. I've been asked, for what base a does the equation $\log_a(x) = a^x$ have only one solution. If

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The Rule of 72: Secrets of the Mathematical Ninja

Despite what you may have heard, Einstein probably never said that compound interest was the greatest force in the universe. It is, however, an interesting beastie. The Mathematical Ninja likes quick fixes. The Mathematical Ninja LOVES estimating powers of e, but he loves quick-and-dirty estimates even more. Especially to one

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A Co-Proof of the Birthday Problem

“[In this context] Co- just means ‘opposite’ — so a co-mathematician is a machine for turning theorems into ffee.” — Miles () Matt Parker () laid down a challenge on Day 1 of the MathsJam conference: he said that proof by MathsJam was acceptable, because if it wasn’t true, you

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Would an infinite number of monkeys eventually write Shakespeare?

“If you had an infinite number of monkeys, there’d be no room for typewriters.” — Jason Arnopp Yes, an infinite number of monkeys would eventually — in fact, before very long at all — write Shakespeare. The problem, then, is finding which of the monkey-poo-smeared manuscripts is actually the whole

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Secrets of the Mathematical Ninja – nth roots (in your head)

I've got a new favourite party trick. It goes like this: "Pick a number1 between 1 and 10 - don't tell me what it is. Pick another number between 1 and 100 - you can tell me that one. Now work out the first number to the power of the

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Secrets of the mathematical ninja: Estimating natural logs

Natural logs are just about the easiest part of the A-level syllabus to look like a god in -- because they're wrongly seen as difficult. In fact, once you know a handful of tricks, you can rattle off things such as 'log of 12 is about 2.5, of course...' (it's

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