Question

vreau sa știu cum se rezolva aceste probleme pentru test.va rog ​

Answer 1

Explicație pas cu pas:

$log_{12}288 - log_{12}2 + log_{2}( lg100 ) = log_{12}(2 \cdot {12}^{2} ) - log_{12}2 + log_{2}( log_{10} {10}^{2} ) = log_{12}2 + log_{12}{12}^{2} - log_{12}2 + log_{2}2 = 2log_{12}12 + 1 = 2 + 1 = 3$

.

$log_{ \sqrt[3]{2} }12 \sqrt[3]{96} = log_{ {2}^{ \frac{1}{3} } }( {2}^{2} \cdot 3){( {2}^{5} \cdot 3)}^{ \frac{1}{3} } = 3log_{2}( {2}^{2 + \frac{5}{3} } \cdot {3}^{1 + \frac{1}{3} }) = 3log_{2}( {2}^{\frac{11}{3} } \cdot {3}^{\frac{4}{3} }) = 3log_{2}{2}^{\frac{11}{3} } + 3log_{2}{3}^{\frac{4}{3} } = 3 \cdot \dfrac{11}{3} log_{2}2 + 3 \cdot \dfrac{4}{3} log_{2}3 = 11 \cdot 1 + 4log_{2}3 = 11 + 4a$

.

$\begin{cases} [x] > 0 \\ [x] \neq 1 \\ x + 2 > 0 \end{cases} \iff \begin{cases} x > 1 \\ x > - 2 \end{cases} \implies x > 1$

$\iff x \in \Big(1 ; +\infty \Big)$