Bài 2:
a. $\frac{x - 1}{-15} = \frac{-60}{x - 1}$ $(1)$
+ ĐK: $x + 5 ≠ 0$ ⇔ $x ≠ -5$.
+ Khi đó: $(1)$ ⇔ $\frac{x - 1}{x + 5} = \frac{6}{7}$
⇔ $\frac{x - 1}{x + 5} - \frac{6}{7} = 0$
⇔ $\frac{7(x - 1)}{7(x + 5)} - \frac{6(x + 5)}{7(x + 5)} = 0$
⇔ $\frac{7x - 7 - 6x - 30}{7(x + 5)} = 0$
⇔ $x - 37 = 0$
⇔ $ x = 37$ (thỏa mãn).
b. $\frac{x - 1}{x + 5} = \frac{6}{7}$
⇔ $7(x - 1) = 6(x + 5)$
⇔ $6x - 7 = 6x + 30$
⇔ $7x - 6x = 30 + 7$
⇔ $x = 37$
d. $(x - \frac{2}{9})^{2} = (\frac{2}{3})^{6}$
⇔ $(x - \frac{2}{9})^{2} = ((\frac{2}{3})^{2})^{3}$
⇔ $(x - \frac{2}{9})^{2} = (\frac{4}{9})^{3}$
⇔ $x - \frac{2}{9} = \frac{4}{9}$
⇔ $x = \frac{4}{9} + \frac{2}{9}$
⇔ $x = \frac{6}{9}$
⇔ $x = \frac{2}{3}$
e. $2^{x} + 2^{x + 4} = 272$
⇔ 2^{x} + 2^{x}.2^{4} = 272$
⇔ 2^{x} + 2^{x}.16 = 272$
⇔ $2^{x}(1 + 16) = 272$
⇔ $17.2^{x} = 272$
⇔ 2^{x} = 272 : 17$
⇔ 2^{x} = 16$
⇔ 2^{x} = 2^{4}$
⇔ $x = 4$
f. $2^{x +4} - 12.2^{x - 2} = 26$
⇔ $2^{x}.2^{4} - 12.\frac {2^{x}}{2^{2}} = 26$
⇔ $16.2^{x} - 3.2^{x} = 26$
⇔ $13.2^{x} = 26$
⇔ $2^{x} = 26 : 13$
⇔ $2^{x} = 2$
⇔ $2^{x} = 2^{1}$
⇔ $x = 1$
g. $\frac{2}{3}.3^{x + 1} - 7.3^{x} = - 405$
⇔ $\frac{2}{3}.3^{x}.3 - 7.3^{x} = -405$
⇔ $2.3^{x} - 7.3^{x} = -405$
⇔ $-5.3^{x} = -405$
⇔ $3^{x} = 81$
⇔ $3^{x} = 3^{4}$
⇔ $x = 4$.
k. $|x + \frac{4}{15}| - |-3,75| = - |-2,15|$
⇔ $|x + \frac{4}{15}| - 3,75 = -2,15$
⇔ $|x + \frac{4}{15}| = -2,15 + 3,75$
⇔ $|x + \frac{4}{15}| = 1,6$
⇔ \(\left[ \begin{array}{l} x + \frac {4}{15} = 1,6 \\ x + \frac {4}{15} = -1,6\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = \frac {4}{3} \\ x = -\frac{28}{15}\end{array} \right.\)
CHÚC EM HỌC TỐT. XIN HAY NHẤT.
