Mathematical Olympiad | Solve and Check Logarithmic Exponential equation | Math Olympiad Training

Can you Solve and Check Logarithmic Exponential equation x^(logx)-100x=0?

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Mathematical Olympiad | Solve and Check Logarithmic Exponential equation | Math Olympiad Training

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[SuperYoonHo]

Thanks so much!!! You are a great help, a huge hero teacher! You have made my math stronger and now i can fully understand the beauty of mathematics and their wonderful construction. This is really amazing. I have upgraded and exeled so much in math. All thanks to you and also some others. May god praise you for all your good work. Love and praiers from YoonHo, South Korea.

[johnwindisch]

Oh and I check your videos everyday. Felix the Cat helps me occasionally but mostly I do them myself.

[johnwindisch]

Was able to solve it !!!!
Thanks to your training!

[davidfromstow]

Absolutely brilliant! (and, no, I couldn't do it! Can't get the hang of logs but I shall persevere) Thank you

[martinwestin]

thanks sir for another amazing question! actually solved it the exact same way as you. keep up the good work!

[JDC]

Note that lgx = log_10(x)

x^(lgx) - 100x = 0

x^(lgx) = 100x
lg(x^(lgx)) = lg(100x)

(lgx)^2 = lg100 + lgx = 2 + lgx
y = lgx
y^2 - y - 2 = 0
(y + 1)(y - 2) = 0
lgx = -1, 2
x = 1/10, 100

[ramanivenkata]

Your working can make even an average student to understand.
Very good explanation

[mohamedabdelkaderahmed]

Dear friend, I'd like to tell you that your respect increases day by day, I like your videos more than you can imagine because you sent me back to sweet days I never forgot, everyday I wait for your new videos not just only for solving or learning new ideas, but more than that, , , so many thanks for you

By the way, I've also solved on the same way you did 😉

[christianthomas]

I think, according to my memories, that 100x could be written as x^(log(100)) and by identification x=100.

[alster]

After recalling the log identities, the rest of the problem is easy.

[owlsmath]

Great problem! I like your thorough explanation

[HappyFamilyOnline]

Very nice explanation👍
Thanks for sharing😊

[lassikokkonen]

I tried to calculate it in my head and I got stuck on t^2-t-2=0 and x=10^t (I can't do quadratic equation in my head)

[smjowci]

what？　log[b](a)
log(10)=log[e](10)
I learned this in japan
Is it wrong?

This movie saying
“log(10)=log[10](10)=1”

I learned
log[10](a): common logarithm
log[e](a): natural logarithm
e: base of natural logarithms