Math-puzzle: How to show that 17^14 > 31^11?

Math-puzzle: How to show that 17^14 > 31^11?

Postby Guest » Sat Mar 09, 2019 10:27 am

Hi!

I know that the power of 17^14 is greater, but I do wonder how you could show it without using obviously any calculation help, but with the mere use of the laws of potency?
I just cannot find even a start and would appreciate any input and any hint.

regards,
Placebo
Guest
 

Re: Math-puzzle: How to show that 17^14 > 31^11?

Postby Guest » Sat Mar 09, 2019 11:34 am

hi

1714==1711*173

if you show:
1711*173 { } 3111
and it is equivalent whit 173 { } 3111 / 1711
and this 3111 / 1711=(31/17)11 [tex]\approx[/tex] 211

now you can compare 173 { } 211
and this you can easy comare

173{ > }211
Guest
 

Re: Math-puzzle: How to show that 17^14 > 31^11?

Postby Placebo » Sun Mar 10, 2019 6:07 am

Hey,
has helped a lot - thanks!:)

Placebo
 
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