Italy - Math Olympiad Problem | A great approach

You should know this approach. Many goes WRONG!
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[@quantumbuddha777]

More efficient method is to cube both sides and swap exponents on the left to get
27^x=x^27, x=27

[@ricordiaerei7776]

Very nice and powerful solution

[@user-yc4wh8lh8b]

Thanks, very good

[@Math9_beheshti]

So useful

[@DebdasBandyopadhyay-yq5jg]

Thanks 🙏 sir

[@techintoshboy3144]

Lowest approx value for x is 1.1508 by using graphical method

[@Limited_Light]

Once you have 3^(x / 9) = x, considering other solutions besides natural numbers are not covered in this approach, why not the following:
3^(x / 9) = 9 * (x / 9)
u = x / 9
3^u = 9u = 3^2 * u
3^(u - 2) = u
Trying u = 1, 2, and then 3, the first solution as a natural number gives us u = 3.
x = 9 * u = 9 * 3 = 27.

[@krishnakalidindi6671]

How? 3^(x/9)=9*(x/9)

[@Limited_Light]

@@krishnakalidindi6671 Did you read my entire comment?

[@krishnakalidindi6671]

@@Limited_Light yes.I could not understand your first step.

[@Limited_Light]

@@krishnakalidindi6671 At time 1:44 , Higher Mathematics has the first step, that I began from, 3^(x / 9) = x.
My change in direction uses x = 1 * x = (9 / 9) * x = 9 * (x / 9). (It's multiplication on the right side, not exponentiation.)
Now that the exponent on the left has a similar form to something on the right, I substituted u for x / 9.

[@krishnakalidindi6671]

It's ok.very good.But it's a trial and error method.Good.

[@prime423]

Outline a plan BEFORE you show a solution. The plan and your thinking are much more important than the grind. In addition, when you use the number one, a vertical line is preferred. In fact, I cant remember any teacher ever using your "1"for 1.

[@Math9_beheshti]

Is there any number else that would have a rule like this

[@nickcellino1503]

This difficult problem can be solved solely by the application of several laws of exponents. My AI software, MathTeacherXL, could not solve the problem even after I provided the answer! Instead of applying the laws of exponents, it tried using logarithms and approximation techniques, all to no avail.

[@user-bi6nd4ty2q]

X=27

[@RealQuInnMallory]

(x ➖ 3x+3)

[@baselinesweb]

Using Lambert W method produces 1.1508. Do you know how to use W method to get 27? Is it another branch?

[@lagomoof]

Yes. 27 comes from the -1 branch. There are infinitely many branches but only the -1 and 0 branches produce real results.

[@AnkushRaj-bl5ye]

I used the Lambert W function to solve this question, but I am getting only 1.151 and -0.8963(which is not possible) as solution and not 27, can anybody tell, why?
Thank you.

[@AbbasGuclu-jn3po]

x=27

[@Maths__phyics]

This is the second time you share the same video

[@DanDart]

What's up with that?

[@DanDart]

This is the same as your 6 days ago video

[@zeroone7500]

your solving method is not complete, if you use Lambert W function there is another solution for x