If logₐb=x, then, by definition of log, aˣ=b. Substituting for x we get a^(logₐb)=b. Substituting for b we get another basic (but more familiar) identity logₐ(aˣ)=x.
x=2 e^x- 1 = x^ 1/log e x e^x/e = x^ log x e (as 1/log a b = log b a /1) e^x/e = e ( a^log a B = B) e^x = e* e ( MULTIPLY BOTH SIDES BY e) e^x = e^2 x = 2 Answer (relating the base)
If we raise both sides to the power ln(x), the equation simplifies to x^x = x². While we get x = 2 as a solution, but also x = 1 which seems kind of correct? Are there any other solutions that may not necessarily be Real?
@@trojanleo123 "what language"... WHAT LANGUAGE???? İ am astonished and ashamed at the same time by the fact that your blindness of mind blocked you away from recognizing the glorious language of 🇹🇷TURKISH🇹🇷, you mere hobbit. WHEN ALLAH CREATED THE EARTH HE MADE EVERYONE SPEAK TURKISH BUT TURKS WERE THE BEST PEOPLE EVER EXISTED AND LET OTHERS SPEAK THEIR OWN LANGUAGE. 🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷 İ am TURKISH 🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷 wth is inflation?? 🇹🇷🇹🇷🇹🇷🇹🇷
I took the natural logarithm of both sides and got x-1=1. From here, the solution is x=2.
Very nice explanation
If logₐb=x, then, by definition of log, aˣ=b. Substituting for x we get a^(logₐb)=b. Substituting for b we get another basic (but more familiar) identity logₐ(aˣ)=x.
Cool!
Take Naperian logarithm:
x-1=[1/ln(x)]ln(x)
=1 --> x=2
I like the second substitution method.
‘E’ to the ‘t’ equals ex-tra terrestrial. 😂😂
x=2
e^x- 1 = x^ 1/log e x
e^x/e = x^ log x e (as 1/log a b = log b a /1)
e^x/e = e ( a^log a B = B)
e^x = e* e ( MULTIPLY BOTH SIDES BY e)
e^x = e^2
x = 2 Answer (relating the base)
OMG, I got one! And I didn't even have to invoke Lambert's W function. Nor his X, Y, or Z functions, either!
Treutel Landing
x = 2.
OMG I can't believe I solved a problem this quickly in seconds. Sometimes I'm impressed with myself. Lol.
You are good! 😍
@@SyberMath Haha. Thank you so much. You are very kind!
Turns out x^(1/lnx) is a constant
Yes, more specifically x^(1/lnx) = e
@@ignaciodecastrofondevila2456 in general x^(1/logb(x))=b for x>0
If we raise both sides to the power ln(x), the equation simplifies to x^x = x². While we get x = 2 as a solution, but also x = 1 which seems kind of correct? Are there any other solutions that may not necessarily be Real?
ln(e^(x-1))=lnx*1/lnx , x-1=1 , x=2 , test , e(2-1)=e , 2^ln2=e ,
Ans 2
Answer is 2 just by looking at it
2? Before vid
Fr it's pretty easy
(e^(x-1)) - x^(1/lnx)în grafiği hakkında desmos graphla 12 dakikalık tartışmamızdan sonra 0^0 = 1 olduğunu öğrendim. Desmos kazandı
Desmos candır! 😍
What is 0⁰ (0 To The Power 0): ua-cam.com/video/kv5VY0REbMg/v-deo.html
@pjb.1775 Just curious what language is that?
@@trojanleo123 "what language"... WHAT LANGUAGE???? İ am astonished and ashamed at the same time by the fact that your blindness of mind blocked you away from recognizing the glorious language of 🇹🇷TURKISH🇹🇷, you mere hobbit. WHEN ALLAH CREATED THE EARTH HE MADE EVERYONE SPEAK TURKISH BUT TURKS WERE THE BEST PEOPLE EVER EXISTED AND LET OTHERS SPEAK THEIR OWN LANGUAGE. 🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷 İ am TURKISH 🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷🇹🇷 wth is inflation?? 🇹🇷🇹🇷🇹🇷🇹🇷
@@trojanleo123 Turkish
@@MichaelRothwell1 Thank you