Question

(0,5p) 2. Numărul natural x care verifică egalitatea:
11.6+5.6+5.62 +5.63 + ... +5.62019 = 36101x este:
A. 3
B.4
C. 5

Answer 1

1 * 6 + 5 * 6 + 5 * $6^{2}$ + .... + 5 * $6^{2019}$ = 5* ( 6 + $6^{2} + 6^{3} + ... +6^{2019}$) +6

$6 + 6^{2} +6^{3} + .... +6^{2019} =$ S | * 6

6S = $6^{2} + 6^{3} + .... + 6^{2020}$

( - )

5S = $6^{2020} -6$

S = $6^{2020} -6$ / 5

= 5* $6^{2020} - 6 /5$ +6

= $6^{2020}$

$\sqrt[2]{6^{2020} }$ = $6^{1010}$

$36^{101x} = 6^{202x}$

202 x = 1010

x = 5