Question

Gasiti n apartine lui N, daca 13*13^3*13^5*.....*13^13=13^n^2

Answer 1

in stanga este 13 la puterea 1+3+5+...+13
suma care este suma de la 1 la 13 - (2+4+6+...+12)
suma de la 1 la n este n(n+1)/2
deci
13*14/2-42 (42 da in paranteza 2+4+6+...+12)
deci 13*7-42=49
13^49=13^n^2
deoarece sunt bazele comune putem scrie
49=n^2
deci n=7 (7^2=49)

Answer 2

se aduna puterile (formula=1+3+5+...+2n-1=n²
2n-1=13 
n=14/2=7
1+3+5+...+13=7²=49

13*13^3*13^5*.....*13^13=13^n^2
13^49=13^n^2
n^2=49
n=7