SOLUTION: (10pow 11) > (11 pow 10) and (20 pow 21) > (21 pow 20)please send the procedure to solve this problem

Question 2447: (10pow 11) > (11 pow 10) and (20 pow 21) > (21 pow 20)please send the procedure to solve this problem

Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
First of all , you put this question in wrong category. Secondly,
you should know how to type power correctly.
We can use logarithm to solve the inequalities.
To show 10^11 > 11^10

Let log be the common logarithm.
log 10^11 = 11,
log 11^10 = 10 log 11 = 10.41392685
Hence, log 10^11 > log 11^10
and so 10^11 > 11^10.
Similarly,
log 20^21 > 21 log 20 = 27.32
log 21^20 > 20 log 21 = 26.44
Hence, log 20^21 > log 20^21
and so 20^21 > 21^20.
Another way:
Consider 11^10/10^10 = (11/10)^10 = (1.1)^10 = (1.1^2)^5 = (1.21)^5
= (1.21)^2 * (1.21)^3 = 1.4641* 1.771561 < 1.5*2 = 3 < 10
Hence, 11^10 < 10* 10^10 = 10^11 and so 10^11 > 11^10.
Consider 21^20/20^20 = (21/20)^20 = (1.05^10)^2 < (1.1^10)^2
< 3^2 < 20
Hence, 21^20 < 20* 20^20 = 20^21 and so 20^21 > 21^20.
Kenny

RELATED QUESTIONS
(10pow 11) > (11 pow 10) and (20 pow 21) > (21 pow 20) is this correct?show the solution (answered by longjonsilver)

A gasoline tank on a tractor holds 18 gallons of gasoline. If the tractor requires 7... (answered by Griffinsdad06)

Hi, I am in need of some help regarding my prediction of a number based from a given... (answered by jim_thompson5910)

please help me solve this problem: theta is an angle is standard position with... (answered by Alan3354)

Need to know if I would add subtract multiply or divide these numbers to get the right... (answered by richwmiller)

2/5[15(-10/11)-20=-8(-10/11)+3(-10/11)-6 or 2/5(15p-20)=-8p+3(p-6) and p=-10/11 (answered by edjones)

Please help me solve this problem: Recorded here are the germination times (in days) for (answered by stanbon)

I have tried every way to solve this and I cannot get it to work. Please help. 3(x-7) =... (answered by Alan3354)

Please help me solve this equation{{{ -21 - (6) + (-3)+... (answered by MathLover1,Tatiana_Stebko)