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.