I love this problem. I love it because it seems so complicated at first, just because we don’t teach students how to attack problems like this in Algebra class. There aren’t any “traditional” methods of attacking it, just a little mathematical reasoning/logic. Here it is:
And this is my new “super duper” problem which I post throughout the year on my board (I use a lot of the same problems each year). I first saw this problem at Messiah College where one of my professors shared it–either Dr. Phillippy or Dr. Brubaker, I can’t remember which.
So give it a try. It’s sure to delight you. My Precalculus class was sharp enough to solve it today in one period (albeit, while I was teaching about a completely different topic :-)).
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At first, that equation does seem difficult and complicated, but only a few seconds pass that I see how to solve it. Something to the itself-power is 1, means that the exponent expression must be equal to zero. From there, simple use of solution to a quadratic equation.
Excuse me, the base and the exponent are two separate expressions. Same principle though, the exponent expression must be equal to zero.