Đáp án:
a) $\frac{x^7}{81}$ = 27 ⇔ $x^{7}$ = 81.27 = $3^{4}$ . $3^{3}$ = $3^{7}$
⇔ x= 3
Vậy x=3
b) $\frac{x^8}{9}$ = 729 ⇔ $x^{8}$ = 729.9 = $3^{6}$ . $3^{2}$ = $3^{8}$
⇔ x= 3
Vậy x=3
c) $5^{x}$ . $(5^3)^{2}$ = 625 ⇔ $5^{x}$ . $5^{6}$ = $5^{4}$
⇔ $5^{x}$ = $5^{4}$ : $5^{6}$ = $5^{4-6}$ = $5^{-2}$
⇔ x= -2
Vậy x= -2
d) (-$\frac{3}{4}$ )$^{3x-1}$ = $\frac{256}{81}$ = $\frac{1}{\frac{81}{256}}$ = $\frac{1}{\frac{3^4}{4^4}}$ = $\frac{1}{(\frac{3}{4})^4}$ = ($\frac{3}{4}$ )$^{-4}$ = (-$\frac{3}{4}$)$^{-4}$
⇒ 3x-1 = -4 ⇔ 3x=-3 ⇔ x= -1
Vậy x= -1
