Question

va rog mult !!!
Exprimati pe x in functie de a
$a = log_{18}24 \\ x = log_{6}12$

Answer 1

[tex]x=\log_6 12=\dfrac{\log_{18} 12}{\log_{18} 6}=\dfrac{\log_{18}\frac{24}{2}}{\log_{18}\frac{24}{4}}=\dfrac{\log_{18} 24-\log_{18} 2}{\log_{18} 24-\log_{18} 4}= \boxed{\dfrac{a-\log_{18}2 }{a+\log _{18} 4}}[/tex]

Si pentru problema de ieri cu inegalitatea.

[tex]\log_a b+\log_b c+\log_c a \ \textgreater \ 3\cdot \sqrt[3]{\log_a b\cdot \log_b c\cdot \log_c a}=\\=3\cdot \sqrt[3]{\dfrac{\lg a}{\lg b}\cdot \dfrac{\lg b}{\lg c}\cdot \dfrac{\lg c}{\lg a}}=3\\ \text{ Deci }\log_a b+\log _b c+\log _c a\ \textgreater \ 3,\forall a,b,c\in(1,\infty )[/tex]