American mathematical Olympiad Question | Olympiad Question solve by @MindyourBRAIN1 #america

Olympiad Question
American mathematical Olympiad question

Solve by @MindyourBRAIN1

#olympiad #algebra #imo #maths #america #american
Olympiad Question
Olympiad

[Denis_Ovchinnikov]

Nice problem, nice solution, but if you don't use logs, it becomes shorter and sweeter.
Let's calculate 1000^(1/x-1/y)=1000^(1/x) /1000^(1/y). The numerator comes from the first term and is equal to 5, denominator is equal to 0.5. Now, the fraction is equal to 10, which immediately means that the answer is 1/3.

[shrutikumari]

This channel is too good for regular practice. You will get amazing tricky questions to exercise your brain 🧠. Productive one. 🤘🏻

[hotspotvry]

I didn't use logarithms. Here's a step to step of my solution:

I.
5^x = 10^3
5 = x√10^3
(0, 5)^y = 10^3
5 = (y√10^3)*10

II.
y√10^3 = 10^3/y
x√10^3 = 10^3/x
10^3/x = 10/^3/y * 10

III.
3/x - 3/y = 1, divided by 3 =
1/x - 1/y = 1/3

[Omeomeom]

so you're using log not like a function where it's log_a(x) = k but instead treating it like it's an exponents (of function composition) where it's log^x_a = k?

[nalapurraghavendrarao]

When explaining, please go little bit slow.