Question

stiind ca log in baza 3din 2=a.Sa se arat ca log in baza 16 din 24=(1+3a)/4a

Answer 1

Stim ca in general se aplica urmatoarea formula
$\log_{a}{b}=\frac{\log_{c}{b}}{\log_{c}{a}}$
Daca inlocuim pe a cu 16, b cu 24 si pe c cu 3 avem
$<span>\log_{16}{24}=\frac{\log_{3}{24}}{\log_{3}{16}}=\frac{\log_{3}{3*2^{3}}}{\log_{3}{2^{4}}}=\frac{\log_{3}{3}+3\log_{3}{2}}{4\log_{3}{2}}=\frac{1+3a}{4a}</span>$