등비수열 로그

$a _{n} = a r ^{n-1}$ $( a > 0 , r > 0 )$라고 하면 $( ar ) ( ar ^{3} ) = 2 ( ar ^{4} )$, $( ar ^{4} ) = ( ar ^{3} ) + 12 ( ar ^{2} )$ $a = 2$, $r ^{2} = r + 12$, $r = 4$, $a _{10} = ar ^{9} = 2 \times 4 ^{9} = 2 ^{19}$ $\therefore$ $\log _{2} a _{10} = \log _{2} 2 ^{19} = 19$