27.$3^{n}$ =243
⇔ $3^{n}$=243:27
⇔$3^{n}$=9
⇔$3^{n}$=3²
⇔n=2
b, Ta có: 4 + 2²+2³+$2^{4}$+....+$2^{20}$=$2^{n}$
⇔ $2^{2}$+ $2^{2}$+ $2^{3}$ +....+$2^{20}$=$2^{n}$
Ta có: $2^{2}$+ $2^{2}$=$2^{2}$.2=$2^{3}$
$2^{3}$.$2^{3}$=$2^{4}$
......
$2^{21}$.$2^{21}$=$2^{22}$
⇒$2^{2}$+ $2^{2}$+ $2^{3}$ +....+$2^{20}$=$2^{n}$
⇔ $2^{21}$.$2^{21}$=$2^{n}$
⇔ $2^{22}$= $2^{n}$
⇔ n=22