Question

Va rog sa ma ajutati. E urgent! Dau coroana​

Answer 1

b) 27=3^3

9= 3^2

3^(2n-3) = (3^3)^7 : (3^2)^2

3^(2n-3) = 3^21 : 3^4 la impartirea cu aceeasi baza, exponentii se scad

3^(2n-3) = 3^17

2n-3=17

2n= 20

n=10

c) 5^(3n+1)= (5^2)^11

5^(3n+1) = 5^22

3n+1=22

3n=21

n=7

d) 7^(n+1-4) = (7^2)^8

7^(n-3) = 7^16

n-3=16

n=19

e) Daca avem aceleasi exponenti, bazele se impart intre ele

(10:5)^(2n+1) = (2^3)^9

2^(2n+1) = 2^27

2n+1 = 27

2n= 26

n= 13

Answer 2

 

$\displaystyle\bf\\ Ex.16\\a)~~\text{\bf Este exemplu de rezolvare.}\\ \\b)\\3^{2n-3}=27^7:9^2\\\\3^{2n-3}=\Big(3^3\Big)^7:\Big(3^2\Big)^2\\\\3^{2n-3}=3^{3\times7}:3^{2\times2}\\\\3^{2n-3}=3^{21}:3^{4}\\\\3^{2n-3}=3^{21-4}\\\\3^{2n-3}=3^{17}\\\\2n-3=17\\2n=17-3\\2n=14\\\\n=\frac{14}{2}\\\\\boxed{\bf~n=7}\\\\=====\\\\c)\\5^{3n+1}=25^{11}\\\\5^{3n+1}=\Big(5^2\Big)^{11}\\\\5^{3n+1}=5^{2\times11}\\5^{3n+1}=5^{22}\\\\3n+1=22\\3n=22-1\\3n=21\\\\n=\frac{21}{3}\\\\\boxed{n=7}\\\\=====$

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$\displaystyle\bf\\d)\\7^{n+1}:7^4=49^{2^3}\\\\7^{n+1}:7^4=49^8\\\\7^{n+1}:7^4=\Big(7^2\Big)^8\\\\7^{n+1}:7^4=7^{2\times8}\\\\7^{n+1}:7^4=7^{16}\\\\7^{n+1}=7^{16}\times7^4\\\\7^{n+1}=7^{16+4}\\\\7^{n+1}=7^{20}\\\\n+1=20\\n=20-1\\\boxed{\bf~n=19}$

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$\displaystyle\bf\\e)\\ 10^{2n+1}:5^{2n+1}=8^9\\\\\frac{10^{2n+1}}{5^{2n+1}}=8^9\\\\\left(\frac{10}{5}\right)^{2n+1}=8^9\\\\2^{2n+1}=8^9\\\\2^{2n+1}=\Big(2^3\Big)^9\\\\2^{2n+1}=2^{3\times9}\\\\2^{2n+1}=2^{27}\\\\2n+1=27\\\\2n=27-1\\\\2n=26\\\\n=\frac{26}{2}\\\\\boxed{\bf~n=13}$

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