Nice Algebra Math Simplification |Find the Value of X

Nice Algebra Math Simplification |Find the Value of X

[dt]

I wasn't good at math. That said, solving this equation was like driving from LA to San Francisco and ending up in Toronto, Canada.

[aimulus]

If complex numbers are allowed as solutions, then there are many more solutions, namely x=(log(3)+2*k*π*i)/log(2) and for every integer k.

[jim]

2^x = u. u^3 + u - 30 = 0. Factor: (u - 3)(u^2 + 3u + 10). Real solution u = 3. Quadratic on the second term for the two complex solutions. Back substitute. Messy problem.

[DreamyCheshire-uprf]

17/1/24 ( Wednesday ) 9.15 pm. Sorry, I failed maths in school. I thought it was a primary school algebra. Never thought that in order to find the value of X, you need to create a value of Y with log included, which I could not comprehend. I was wrong to think that the value of X was 3. Instead, after so many steps, the value of X was another wonder I failed Maths.

[marol]

Nice solution, but way too long! Don't make your lifes harder than necessary:

At time 02:30, just compare the coefficients:
y^3 + y = 3^3 + 3
<=> y = 3
<=> 2^x = 3
<=> x = log3 / log2

(+ saved 10 minutes 😊)

[francescob.]

The thumbnail got me very intrigued, and I accepted the challenge.
I solved it on my own, and I managed to find x = 3 in a much simpler way.
I still applied substitution, t = 2^(x), so x = log_2(t). But when I reached t^(3) + t = 30, i scomposed left and right side into t (t^(2) + 1) = 2*3*5
And 2*3*5 = 2 (3*5) = 3 (2*5) = 5 (2*3), so I had to choose the only combination that would match the left side, and the only one that matches is 3 (2*5). In fact, 3 * (3^(2) + 1) = 30.

So t = 3, and x = log_2(3) .

But then, when I confronted it to the solution you gave, I realized that I found only the real solution. Was it sheer luck because logarithm is defined only for real numbers, or my solution had some sense?

[alexxander]

This was definitely the long way in my opinion. I definitely forgot the other way tho. Too many things you just have to know like 2^3 is 8 and breaking 30 in to 27 and 3.
M.

[iangray]

I'm amazed at how many people get an answer of 3 while completely misunderstanding the nature of logs or that x is a power. The right answer for the wrong reason is the wrong answer.

[BarrieHughes]

You could apply the log formula right at the start.

[jropar]

I don't think that anyone who was worried about the music has the patience for the math. Just my opinion. Thank you so much. That was a lot of work. When you're buried in the math, anything else should fade to oblivion.

[praiseYAHalways]

soooo X = 3 as in 8x3 (24) plus 2x3(6) equals 30???? at least that's how I did it in my head....took about 5 seconds maybe less 🤔 unless I'm reading the problem wrong...

[MathHero]

let u = 2^x. Then u^3+u =30. derivative of u^3+u is 3u^2+1 which is positive. Therefore, LHS is increasing and the equation has at most one solution. u=3 is an obvious guess. x = log(3)/log(2) is the only solution then!

[Daimler]

Спасибо за познавательное видео уровнения такого уровня были когда поступал в технический университет в России в 1999 году. Тренировался считал десятками такие. Сейчас уже конечно подзабылись формулы, но с учебником думаю решил бы и сейчас.

[miguelorobitg]

One in top righ of eight, another one in top right of number two. I found two of them! Genius!

[paulssamuel]

let y=2^x
then y^3 + y = 3^3 + 3
=> y=3
=> x = log3/log2

[troubledsole]

Knowing the theorems was essential to solving for X.

[stephenremo]

Like you can solve in 5 seconds in your head ...
Or 10 pages of math

[jcolivie]

Is this the easiest way? So I prefer to study integral calculus, differential calculus, theoretical physics because they are much easier than that (contains irony).

[ezrapotter]

Right off the bat, x<2 since 8^2 is 64

[MounikaMix]

Can we not directly apply log to the main equation and solve