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Radical Exponents

Recently I saw this from brilliant.org on Facebook and it struck me as an interesting problem:

the first solution is trivial and obvious:

But the Facebook post said there was two, so I set out in search of the next one. As there were exponents I thought I’d take logs of both sides:

Then realised I could take logs to base X and make things a whole lot simpler….

So x = 9/4

As you can see it reduces to an easily solvable problem, and all that was left was to check the answer:

A lovely little problem that gives a good work out to algebra and log skills.

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  1. July 7, 2016 at 1:28 pm

    x√x=x^1.5
    √x=1.5
    x=2.25

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