[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]
