Question

Comparati numerele:a)10^100si 100^10 b)3^45si2^30 c)6^120si5^80 d)200^30 si 8^10•10^60 e)3^55 si 2^88

Answer 1

a)   10¹⁰⁰ si  100¹⁰ = ( 10² )¹⁰ = 10²⁰

10¹⁰⁰ >  10 ²⁰ ==>    10¹⁰⁰ >  100 ¹⁰

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b)   3⁴⁵ si 2³⁰

3⁴⁵ = ( 3³ ) ¹⁵ = 27¹⁵

2³⁰ = ( 2² ) ¹⁵ = 4¹⁵

27¹⁵ >  4¹⁵ ==>  3⁴⁵ > 2³⁰

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c)    6¹²⁰  si 5⁸⁰

6¹²⁰ = ( 6³ ) ⁴⁰ = 216⁴⁰

5⁸⁰ = ( 5² )⁴⁰ = 25⁴⁰

216⁴⁰ >  25⁴⁰ ==>    6¹²⁰ >  5⁸⁰

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d)   200³⁰  si   8¹⁰ x 10⁶⁰

8¹⁰ x 10⁶⁰=  ( 2³) ¹⁰ x ( 10²) ³⁰= 2³⁰ x 100³⁰ = ( 2 x 100)³⁰ = 200³⁰

==>   200³⁰  =  200³⁰ ==>   200³⁰ = 8¹⁰ x 10⁶⁰

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e)   3⁵⁵   si 2⁸⁸

3⁵⁵ = ( 3⁵ ) ¹¹ = 243¹¹

2⁸⁸ = ( 2⁸ )¹¹ = 256¹¹

==>    243¹¹ <  256¹¹ ==>   3⁵⁵ <  2⁸⁸