[tex]\displaystyle\\
1)\\
b_5=b_1\times q^{5-1}=b_1\times q^4=48\\\\
b_8=b_1\times q^{8-1}=b_1\times q^7=384\\\\
\text{Descompunem numerele 48 si 384 in factori primi:}\\\\
48=3\times16=3\times2^4=b_1\times q^4\\\\
384=3\times128=3\times2^7=b_1\times q^7\\\\
\Longrightarrow~\boxed{\bf b_1=3}~~\text{ si }~~\boxed{\bf q=2}\\\\
3)\\
32^x=16\cdot2^x\\\\
\frac{32^x}{2^x}=16\\\\
\frac{\Big(2^5\Big)^x}{2^x}=2^4\\\\
\frac{2^{5x}}{2^x}=2^4\\\\
2^{5x-x} = 2^4\\\\
2^{4x} = 2^4\\\\
4x=4\\\\
x=\frac{4}{4}=\boxed{\bf1}
[/tex]
