Here is a question I did when learning algebra thorugh the AoPS Intro to Algebra TEXTBOOK

Don't worry, this is from the textbook I'm self-learning and I've solved it.

This is also from an AMC12 so it's not a violation of copyright since I'm citing it

It's good for a exponent refresher.

Latex isn't working so here's the photo.

This should be relatively easy for the moderators and probably some of the regular users too

I did it in 3 minutes, my parents in like 30 seconds LOL

hugomimihu May 14, 2020

#1**+3 **

5^(48/x) 1

_________________ = ____

5^(26/x) * 25^(17/x) 25^2

5^(48/x - 26/x) 1

_____________ = ______

(5^2)^(17/x) 25^2

5^( 22/x) 1

_______ = ________

5^(34/x) (5^2)^2

1 1

_______ = _____

5^(12/x) 5^4

Which implies that 12/x = 4 ⇒ x = 3

CPhill May 14, 2020

#2**+2 **

THis is how I did it(or similar, this is from a few days ago, doing it now)

So we first convert all 25^whatevers into 5^somethings

so

5^-4 = 5^48/x OVER 5^26/x * 5*34/x = 5 ^(48-26-34)x = 5^-12x

so -12x = -4, x = 3

essentially the same as what you did

And also I'd nominate your answer for "Best Answer"

hugomimihu
May 14, 2020