Question

Determinati numarul n penru care au loc egaliratile :
b)3la2ori n-3=27la7:9la2

c)5la3ori n+1=25la11

d)7la n+1 :7la4 =49la8

e)10la2ori n+1:5la2ori n+1=8la9

la=la putere
Dau coroana

Answer 1

[tex]5^{3n+1}=25^{11}\Leftrightarrow5^{3n+1}=5^{22}\Leftrightarrow 3n+1=22\\ \Leftrightarrow 3n=21\Leftrightarrow n=7\\ 3^{2n-3}=27^7:9^2\Leftrightarrow 3^{2n-3}=3^{21}:3^4\Leftrightarrow 3^{2n-3}=3^{21-4}\\ 2n-3=17\Leftrightarrow 2n=20\Leftrightarrow n=10\\ 10^{2n+1}:5^{2n+1}=8^9\Leftrightarrow 2^{2n+1}=2^{27} \Leftrightarrow 2n+1=27\Leftrightarrown=13 [/tex]
Pe al treilea fa-l singur: il scrii pe 49 ca 7^2 si obtii in final n=19. trebuie sa stii foarte bine proprietatile operatiilor cu puteri! 

Answer 2

b. 3²·n-3=[3³]⁷/[3²]²
⇒3²·n-3=3²¹/3⁴
⇒3²·n-3=3¹⁷
⇒3¹⁷=3¹⁷⇒2n-3=17
⇒2n=20
⇒n=10∈N;
c. 5³·n+1=[5²]¹¹
⇒5³·n+1=5²²
⇒5²²=5²²⇒3n+1=22⇒3n=21⇒n=7∈N;
d. 7 la n+1  /7⁴=[7²]⁸
⇒7 la n+1  /7⁴=7¹⁶
⇒7 la n+1=7²⁰
⇒7²⁰=7²⁰⇒n+1=20⇒n=19∈N;