Logaritm

Stefy Dum Noi 04, 2012 7:47 pm

Ma puteti ajuta la aceste exercitii? Sad

Daca se poate, cat mai explicit...Multumesc! Neutral

1. $49^{\frac{1}{2}log_{7}\frac{1}{4}}=$

2. $-log_{2}(log_{3}\sqrt{\sqrt[4]{3}})=$

3. $log_{\frac{1}{2}}0,5 \cdot log_{0,3}0,09=$

Thank You

**Admin** Mar Noi 06, 2012 9:56 pm

Problema 1)
${49^{\frac{1}{2}lo{g_7}\frac{1}{4}}} = {\left( {\frac{1}{4}} \right)^{{{\log }_7}{{49}^{\frac{1}{2}}}}} = \frac{1}{4}$

**Admin** Mar Noi 06, 2012 10:00 pm

Problema 2)
$\begin{array}{l} - {\log _2}\left( {{{\log }_3}\sqrt {\sqrt[4]{3}} } \right) = - {\log _2}\left( {{{\log }_3}{{\left( {{3^{\frac{1}{4}}}} \right)}^{\frac{1}{2}}}} \right) = - {\log _2}\left( {{{\log }_3}{3^{\frac{1}{8}}}} \right) = - {\log _2}\frac{1}{8}\\ = {\log _2}8 = 3 \end{array}$

Problema 3) tema!
Toate aceste probleme se rezolva relativ simplu.... folosind proprietăți elementare ale logaritmilor.

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