2
a) [tex][(-9)^{n}]^{2}=81^3[/tex] . In acest caz pentru usurinta schimbam locul puteriilor 2 si n:
[tex][(-9)^{2}]^{n}=81^3 <=> 81^n=81^3 => n=3[/tex]
b) [tex](+8)^n*(-3)^n=(-24)^6[/tex]. 24 poate fi scris ca si 8*3 si atunci avem:
[tex](+8)^n*(-3)^n=(-3*8)^6[/tex]<=>[tex](+8)^n*(-3)^n=8^6*(-3)^6 => n=6[/tex]
c) [tex](-8)^n*(+18)^n=(-144)^5[/tex] <=> [tex](-8)^n*(+18)^n=(-8*18)^5 <=> (-8)^n*(+18)^n=(-8)^5*(18)^5[/tex] => n=5
d) [tex][(-12)^2]^n=144^3 <=> 144^n=144^3 => n=3[/tex]
5
a) 3x+5-2(x+2)=8-3(1-x) <=> 3x+5-2x-4=8-3+3x <=> x-1=5+3x <=> -2x=4 <=> x=-2
b) 3(2x+1)-4(x+3)=5-2(2x+1) <=> 6x+3-4x-12=5-4x-2 <=> 2x-9=3-4x <=> 6x=12 <=> x=2
