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Nice problem, but the thumbnail is wrong

Very clear info. explanation-Segaran M'sia

Done,shorter

1/9 ok

Very ex

Good

Excelente

Good

Good

0.5

excelente

¿Podrías hacer un video demostrando las propiedades de los logaritmos? Could you make a video demonstrating the properties of logarithms? Thank you so much

Muy bueno

Todos los días venís tus ejercicios. Un saludo desde España

B. 1

Muy bueno.

(1) x^(x^999) = 999 Let y=x^999, then x^y=999 (2) x^(x^y) = x^999=y Compare (1) an (2), 999=y=x^999 So x=999^(1/999)

You referenced this being from an olympiad and the rule everybody misses is referencing the source...

Easy to figure out in one's head and fun to verify with the multiple choice.

Excellent that you bothered to verify the answer unlike a lot of mathematics RUclipsrs! Nice explanation.

Excelente

if it is x^(x^999) then it's true but if it is (x^x)^999 then it's false , it's confusing and my head hurts for something that simple

Excelente

I would substitute 4^x at 1:15

Once you get 3x = sqrt(x)/2, just square both side. 36x^2-x=0 or 36x=1 or x=1/36. Why go thru a lengthy process? This is nowhere near Olympiad level.

why is x = 1/2 wrong? 8 = 2^3 and the square root of that is 1/2 so the bases are the same: 2^3 on the left and right. so that leaves you with x = 1/2

bueno

Spectacular! I did it!

Mam but √x = -2 does not make sense becoz if we square we get x = 4 and if we reverse it we get √x = 2

Good job my teacher!

Lo hiceeeee

Maravilloso.

Lo hiceeee thanks

Good job!

Good

Nice❤

Good job my teacher!

We can find x in a simpler way. sqrt(12) / 3^x = 18 <=> sqrt(12) * 3^(-x) = 18. So, we square the equality => 12 * 3^(-2x) = 324 3^(-2x) = 324/12 3^(-2x) = 27 3^(-2x) = 3^3 Now we can solve a simple linear equation -2x=3 => x=-1.5

5

Very NICE exercise which shows there was a trap: 10^5^x = 10^(5^x) and not (10^5)^x 10^5^x = 5 carreful (recall): 10^5^x = 10^(5^x) and not (10^5)^x 10^5^x = 10^(log(5)) same base (= 10) 5^x = log(5) log(5^x) = log(log(5)) x·log(5) = log(log(5)) ----- final result ----- ■ x = log(log(5))/log(5) ■ x ≈ -0.222529 🙂

Good job!

Good job!

Good job!

Very good job my teacher!

Good job my teacher!

Your consistent commitment to spreading positivity is changing the game. Kudos!

2√6: 😔

Good job!

How much she earns by video is not your business. Let’s me tell you, I am a math teacher. With her videos, I learned a lot of things and I became stronger in my math knowledge.