1. ## exponents

Solve for x: 2^x + 6^x + 16^x = 7^x + 8^x + 9^x.

Is there an algebraic way to solve for x? My way of solving this is through graphing.

2. Well I'd have to say that just by looking at it, 0 is a solution:

$\displaystyle 2^0 + 6^0 + 16^0 = 7^0 + 8^0 + 9^0$

$\displaystyle 1 + 1 + 1 = 1 + 1 + 1$

$\displaystyle 3 = 3$

Also 1 is a solution since all those numbers add to 24:

$\displaystyle 2^1 + 6^1 + 16^1 = 7^1 + 8^1 + 9^1$

$\displaystyle 24 = 24$

However, beyond that, I do not know. There might be more than 2 solutions, but maybe whoever gave you this problem didn't think of that. I'd say look at the solutions of 1 and 0 if you have a problem like this, and go from there. In my opinion this looks like a thinking problem, something you're just suppose to see.

3. I think you already found all the integer solutions, based on my graph.

4. I think you already found all the integer solutions, based on my graph. I did not see well as you did. I thought it needs higher analysis . . . . i lacked insight on that, SEEING what is the obvious.

Actually, i found that problem in one website a year ago, that i can no longer locate. It intrigues me, so i copied it in one of my notes.

5. No worries, they take practice. You'll know what to look for next time. Plus 0 and 1 tend to be common solutions so trying those never hurts.