Question

Daca $log_{2}$ 3 = a , sa se afle $log_{24}$ 54

Answer 1

$\log_{24}54=\frac{\log_{2}54}{\log_{2}24}=\\ \\=\frac{\log_{2}3+\log_{2}3+\log_{2}3+\log_{2}2}{\log_{2}2+\log_{2}2+\log_{2}2+\log_{2}3}=\\ \\=\frac{a+a+a+1}{1+1+1+a}=\\ \\=\frac{3a+1}{3+a}$

Am folosit:

$\log_{a}b=\frac{\log_{c}b}{\log_{c}a}$

si

$\log_{a}x+\log_{a}y=\log_{a}(xy)$