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

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

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?

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 $$\approx$$ 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?

Hey,
has helped a lot - thanks!:)

Placebo

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Joined: Sat Mar 09, 2019 8:45 am
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### Re: Math-puzzle: How to show that 17^14 > 31^11?

$$17^{14}> 31^{11}$$ if and only if
$$14log(17)> 11log(31)$$ which is true if and only if $$\frac{14}{11}> \frac{log(31)}{log(17)}$$.

$$\frac{14}{11}= 1.272727272727272...$$
and
$$\frac{log(31)}{log(17}= 1.21204681309626$$.
Guest