ARRANGE THE NUMBERS 2847, 3539, 5363, 7308 AND 11242 FROM...

1. Arrange the numbers 2

⁸⁴⁷

, 3

⁵³⁹

, 5

³⁶³

, 7

³⁰⁸

and 11

²⁴²

from the largest to the

smallest.

【Solution】

Since 7

⁴

= 2401 3 > =

⁷

2187 > 2

¹¹

= 2048 , we have 7

^{4 77}

^×

> 3

^{7 77}

^×

> 2

^{11 77}

^×

.

Since 2

⁷

= 128 > = 5

³

125 11 >

²

= 121 , we have 2

^{7 121}

^×

> 5

^{3 121}

^×

> 11

^{2 121}

^×

.

It follows that 7

³⁰⁸

> 3

⁵³⁹

> 2

⁸⁴⁷

> 5

³⁶³

> 11

²⁴²

ANS: 7

³⁰⁸

> 3

⁵³⁹

> 2

⁸⁴⁷

> 5

³⁶³

> 11

²⁴²