请教JJ数学第186题

gina2012

for the sake of rp

the way i do it

4 ^16 = 4^16 * (5/4) ^15 * (4/5) ^15=5^15 * 4 *  (4/5) ^15

The quesiton become if  4 *  (4/5) ^15 >1 or not

it is actually 0.8 ^15 > 0.25 or not

it is obvious 0.8 ^15 is smaller than 0.25

JNC913

for the sake of rp

the way i do it

4 ^16 = 4^16 * (5/4) ^15 * (4/5) ^15=5^15 * 4 *  (4/5) ^15

The quesiton become if  4 *  (4/5) ^15 >1 or not

it is actually 0.8 ^15 > 0.25 or not

it is obvious 0.8 ^15 is smaller than 0.25

-- by 会员 gina2012 (2012/5/25 21:42:13)

awesome, thanks!

JNC913

I think I just came up with an another way to solve this type of problem, the logic applies to similar comparing category:

Find the same factor in the two numbers, for this problem: whether 4^16 > 5^15, we can make
1. 5^15 in the side of 4^16,
    or
2. 4^16 in the side of 5^15.


Let's take 1:
4^16= 4^16 * 5^15 * (1/5)^15 = 4* (4/5)^15 * 5^15, the rest of the steps will be the same as above discussed.


Sames for option 2.


Hope this hopes.