A Cool Exponential Equation

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[@carly09et]

x == 1/2, I could not find a 'clean' way to solve this. I 'guessed' making (1+1/x) as 3 and checked.

[@mcwulf25]

Even Syber's solution is like this. You will only get full marks by showing it's the only solution, though!

[@YMariusChivuY83]

❤❤ x=1/2 one of the eq.'s solutions.

[@Hobbitangle]

First, we squaring both sides of the equation, resulting to the equation with integer coefficients and integer right side. So we may assume that the expression in parentheses is also integer, as well as the exponent, because otherwise will get rational or even irrational value. So 1+1/x = m, 2•x + 2 = n, and m^n = 27 last equation had only two solutions in integers: m=n=3 and m=27, n=1 substituting we'll see that only the first option satisfies the equation. So the answer is x = 1/2

[@nicolasstichel1386]

You can actually rewrite x+1 as (1+1/x)*x. You can also rewrite the left side as 3^3^1/2 Hence the left side becomes (1+1/x)^(1+1/x)^x = 3^3^(1/2). From here you can easily see and check that (1+1/x) = 3 or x=1/2. It is fortunate but easily the fastest way to solve it, I believe. :) The analysis regarding other potential solutions needs to be done as explained in the video.

[@gdtargetvn2418]

Noice

[@TDSONLINEMATHS]

Nice

[@lucas0_03]

Make a video solving the equation: e^x=3x+2

[@yoshinaokobayashi1557]

sqrt(27)=3^(3/2)=(1+2)^(3/2), then x=1/2 is one answer. Fin.

[@garydudley6149]

I solved it 1 day ago.

[@Paul-222]

Write (1 + 1/x) as (x+1)/x and SQRT(27) as 3^3/2. Set the bases equal to each other and the exponents equal to each other, and solve for x. Takes less than a minute that way.

[@ibrahemiden2307]

*I solve it by guessing in 30 seconds*

[@mohkh7610]

I am only high school level and I didn't take about euler's number so can anyone make me understand at 5:32 how 1/x when approaching infinity becomes 0 and not not defined?

[@KAI-wn1pg]

If it approaches infinity the base becomes very very very large so 1/very large->0 so it becomes 0 It is undefined when x->0

[@mohkh7610]

@@KAI-wn1pg Thanks

[@mcwulf25]

I can see x = 1/2 just by comparing the LHS to 3^(3/2).

[@Chrisoikmath_]

Yesterday t=-x Today t=1/x

[@yakupbuyankara5903]

X=1/2.

[@Caloteira1665]

Vc tá me matando caraaaaaaaaaaaaaaaaaaaaaaaa😮😮😮😮😢😂😢😂😮😂!!!! Depois de ver seu canal eu bato o olho na questão e sei resolveeeeeerrr!!!!!!!😭😭😭😭🧐🧐

[@kianmath71]

1/2

[@andylee63]

Without watching the video, I have a solution that leads to an easy guess and check. That is the best I can do. Let's see the video...

[@andylee63]

...I used t as well, but my t was (1 + 1/x). Same result, of course.

[@SyberMath]

nice

[@iRReligious]

Guessing is not a good solution!!

[@SyberMath]

Why not?

[@broytingaravsol]

x=1/2

[@bramont6225]

Gracias por las dos clases profesor de este día la de geometría y la presente. Perdone como se llama su cuaderno electrónico, nuevamente gracias.

[@mathswan1607]

x=1/2

[@rakenzarnsworld2]

x = 1/2