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anonymous
 one year ago
dear Champions ! give me please an explication  thank you  what is larger :
A = 2^3^4 or B = 4^2^3 ?
 how can i deciding that in case of A or in case of B the top exponent is an exponent of the bottom number ,in case A of 2 or in case B of 4 , or are exponent of the first exponent,in case A ,of 3 or in case B of 2 ?
anonymous
 one year ago
dear Champions ! give me please an explication  thank you  what is larger : A = 2^3^4 or B = 4^2^3 ?  how can i deciding that in case of A or in case of B the top exponent is an exponent of the bottom number ,in case A of 2 or in case B of 4 , or are exponent of the first exponent,in case A ,of 3 or in case B of 2 ?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Dear Champions this was what have surprised me in Brilliant.org ,math. forum when i have wrote for above exercise that are equal A and B  so this was a correct accepted answer but after this i have got a second exercise what was : (6x)^6 = 6^2^3 and for this equation i have wrote like firstly very easy root x=1  so this was what have surprised me when have got the answer that x=1 is wrong so that not is root of this equation  i dont understand it why ? can somebody explaining me please ? thank you very much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0 so than i remember right again the accepted correct root was x= 6^(1/3)  why ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(2^{3^4}\) or \((2^3)^4\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you mean \(2^{3^4}\) then consider \(4^{2^3}=2^{2\cdot2^3}=2^{2^4}\) so clearly \(2^{3^4}>2^{2^4}\) since \(3>2\implies 3^4>2^4\implies A=2^{3^4}>2^{2^4}=4^{2^3}=B\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$(6x)^6=6^{2^3}\\6^6 x^6=6^8\\x^6=6^2\\x^3=\pm6\\x=\pm\sqrt[3]{6}$$

dan815
 one year ago
Best ResponseYou've already chosen the best response.0perhaps trying to find a generalization for this is more intriguing

dan815
 one year ago
Best ResponseYou've already chosen the best response.0like does this hold for all consecutive numbers

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first one is exactly what I wrote; I don't understand why you just drew it out...
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