Punctul a)
[tex] 4^{2x+1} +4^{2x+3} +16^{x+1} =1344 \\ 2^{4x+2} +2^{4x+6} +2^{4x+4} =1344 \\ 2^{4x+2} (1+2^4 +2^2 ) =1344 \\ 2^{4x+2} \cdot 21 =1344 \\ 2^{4x+2} =64 =2^6 \\ 4x+2 =6 \\ 4x=4 \\ \tt x=1 [/tex]
Punctul b)
[tex] 3^{2x+5} -3^{2x+3} -3^{2x+1} -3^{2x} =1908 \\ 3^{2x} (3^5 -3^3 -3^1 -1 ) =1908 \\ 3^{2x} (216-4) =1908 \\ 3^{2x} \cdot 212 =1908 \\ 3^{2x} =9=3^2 \\ 2x=2 \\ \tt x=1 [/tex]
Punctul c)
[tex] 9^{12x} +81^{6x} +27^{8x} =3\cdot 81^{12} \\ 3^{24x} +3^{24x} +3^{24x} =3\cdot 3^{48} \\ 3\cdot 3^{24x} =3\cdot 3^{48} \\ 3^{24x} =3^{48} \\ 24x=48 \\ \tt x=2 [/tex]
Punctul d)
[tex] 2^{3x} +2^{3x+1} +2^{3x+2} +2^{3x+3}+2^{3x+4} =1984 \\ 2^{3x} (1+2+2^2+2^3+2^4) =1984 \\ 2^{3x} (2^5-1) =1984 \\ 2^{3x} \cdot 31 =1984 \\ 2^{3x} =64=2^6 \\ 3x=6 \\ \tt x=2 [/tex]
Nu sunt 100 de puncte ..
