Japan | A Nice Algebra Problem | Math Olympiad

Hello My Dear CZcams Family 😍😍😍
Hope you all are doing well 🥰🥰🥰
If you are enjoying my video about how to solve this math olympiad algebra problem then please Like and Subscribe my channel as it helps me a lot 🙂🙂🙂

[@Beinglogical321]

Nice vedio

[@soniamariadasilveira7003]

Gostei muito!

[@2012tulio]

Just log both sides and continue.. easy

[@user-ee7nw2rx9s]

По какому основанию логарифмировали?

[@prollysine]

5^k=6 , k*ln5=ln6 , k=ln6/ln5 , 5^(x+6)=5^((ln6/ln5)*(x+5)) , x+6=(ln6/ln5)(x+5) , (ln6/ln5)x -x=6-(ln6/ln5)*5 ,
x*((ln6/ln5)-1)=6-5*ln6/ln5 , x=(6-5*ln6/ln5)/(ln6/ln5-1) , x=~ 3.82747 ,
test , 5^(3.82747+6)=~ 7.39786*10^6 , 6^(3.82747+5)=~ 7.39786*10^6 , same , OK ,

[@user-ee7nw2rx9s]

@@prollysine ln6/ln5=log(5)6

[@epsi]

Too bad there's no way to rationalize a denominator involving logarithms, like how you can multiply a square root by its conjugate. 🫤
Btw,
x = -5 + log(5) / [log(6) - log(5)]
and
x = -5 + log_{6/5}(5)
both look nicer to me than
x = [5log(6) - 6log(5)] / [log(5) - log(6)]
but that's just my opinion, and i'd agree that making it look nicer is an unnecessary step.