How powerful is power?
If x x = 2 0 1 5 , then which answer is equivalent to x x x x ?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
No tenía conocimiento de esta regla o propiedad de las potencias. Puede darme una referencia para leer acerca de esto. Gracias.
Log in to reply
En el link de Sandeep Bhardwaj tienes las propiedades, pero si quieres saber más sobre el tema, te recomiendo el siguiente artículo de Wikipedia: https://en.m.wikipedia.org/wiki/Tetration
log(x^{x^{x^{x}}})=x^{x}log(x^{x}). As, x^{x}=2015, so, log(x^{x})=log(2015). So, log(x^{x^{x^{x}}})=2015 \times log(2015)=log(2015^{2015}). Hence, x^{x^{x^{x}}}= 2015^{2015}.
What is the error in the above?
Log in to reply
You cannot take the coefficient of the log of x^{x^{x^{x}}} as x^{x}, because it is not the power of the brackets of the log, the power of the log's brackets is x^{x^{x}} because there's only one x in the base. If it was {x^x}^{x^x} it would've worked as this will be simplified to x^{x{x^x}}.
You actually can evaluate it further. Using Excel's Goalseek function, you can find that for x^x to = 2015, x must equal 4.83072469611793. Then it's just a matter of plugging it in to get 1.28303*10^77. I'm sure there's some truncated digits, though I'm an engineer so I only deal with rounded numbers anyways :)
What I'm wondering, is there a function for finding x for a problem like this, or iteration the only way to find a solution?
Tengo dudas al respecto.
But isn't (((x^x)^x) ^x) = x^(x^3)?
Log in to reply
Try pluggin in some values eg 2 and see what happens
(((x^x)^x)^x) is but the question was (x^(x^(x^x))). You always work from top to bottom.
Yes, but x x x x = x ( x ( x x ) )
x x x x = ( ( ( x x ) x ) x )
You have to respect the operators priority.
x x = 2 0 1 5 ⇒ x x x x = x x 2 0 1 5
Note that by convention, calculations start from top to bottom.
can u explain this questio??
Log in to reply
The following article from Wikipedia talks about towers of powers: https://en.m.wikipedia.org/wiki/Tetration
Hope that helps...
Log in to reply
For your this act of kindness I follow back you Thanks!!!
I have added a statement. Is that what you are expecting?
Log in to reply
But Where Is Your statement?? thanks!
Log in to reply
@Nazir Balti – "Note that by convention, calculations start from top to bottom."
Reminding the notion of tower rule , the powers are evaluated from the top (of the tower of powers) down to its bottom.
Substituting the value x x = 2 0 1 5 into the required expression at the top, we get x x 2 0 1 5 . □
CAUTION:
We can't evaluate it further to 2 0 1 5 2 0 1 5 because we work from top to down, therefore taking the previous step, first we need to evaluate x 2 0 1 5 , unknown to us. Hence we can't jump to the conclusion of 2 0 1 5 2 0 1 5 .
enjoy!