Question

cum se face punctul c??

Answer 1

Explicație pas cu pas:

$3 \cdot {16}^{x} + 2 \cdot {81}^{x} = 5 \cdot {36}^{x} \ \ \Big|:{36}^{x}$

$3 \cdot { \bigg( \dfrac{4}{9} \bigg)}^{x} + 2 \cdot { \bigg( \dfrac{9}{4} \bigg)}^{x} = 5$

$3 \cdot { \bigg( \dfrac{4}{9} \bigg)}^{x} + 2 \cdot { \bigg( \dfrac{4}{9} \bigg)}^{ - x} - 5 = 0$

$not \breve{a} m \ \ { \bigg( \dfrac{4}{9} \bigg)}^{x} = t$

$3 \cdot t + 2 \cdot \dfrac{1}{t} - 5 = 0$

$3 {t}^{2} - 5t + 2 = 0$

$(3t - 2)(t - 1) = 0$

$3t - 2 = 0 \iff t = \dfrac{2}{3} \iff { \bigg( \dfrac{4}{9} \bigg)}^{x} = \dfrac{2}{3}$

${ \bigg( \dfrac{2}{3} \bigg)}^{2x} = { \bigg( \dfrac{2}{3} \bigg)}^{1} \iff 2x = 1 \implies \bf x = \dfrac{1}{2}$

$t - 1 = 0 \iff t = 1 \iff { \bigg( \dfrac{4}{9} \bigg)}^{x} = 1$

${ \bigg( \dfrac{4}{9} \bigg)}^{x} = { \bigg( \dfrac{4}{9} \bigg)}^{0} \implies \bf x = 0$