Question

$Sa~se~calculeze: \\ lg__{24} 2~in~functie~de~c=log__{24}3$

Answer 1

$c=log_\big{24}3\\\\log_\big{24}2 = \dfrac{log_\big{3}2}{log_\big{3}24} = \dfrac{log_\big{3}2}{\dfrac{1}{log_\big{24}3}} = \dfrac{log_\big{3}2}{\dfrac{1}{c}} = c\cdot log_\big{3}2 \\ \\ \\ \Rightarrow\boxed{ log_\big{24}2 = c\cdot log_\big{3}2}$

Answer 2

$\displaystyle Folosim~identitatea ~\boxed{\log_ab \cdot \log_bc= \log_ac}.\\ \\ \log_{24}2= \log_{24}3 \cdot \log_32=c \cdot \log_32.$