1, (2x)² = 81
⇒ 2x = 9 hoặc 2x = -9
⇒ x = $\frac{9}{2}$ hoặc x = $\frac{-9}{2}$
Vậy x = $\frac{9}{2}$ hoặc x = $\frac{-9}{2}$
2, ($\frac{1}{2}x$)² = $\frac{49}{81}$
⇒ $\frac{1}{2}x$ = $\frac{7}{9}$ hoặc $\frac{1}{2}x$ = $\frac{-7}{9}$
⇒ x = $\frac{14}{9}$ hoặc x = $\frac{-14}{9}$
Vậy x = $\frac{14}{9}$ hoặc x = $\frac{-14}{9}$
3, 9x² = 100
x² = $\frac{100}{9}$
$x^{2}$ = $(\frac{10}{3})^{2}$
⇒ x = $\frac{10}{3}$
Vậy x = $\frac{10}{3}$
4, $\text{(x - $\frac{1}{3}$)}^{2}$ = $\frac{1}{36}$
⇒ $\text{x - $\frac{1}{3}$}$ = $\frac{1}{36}$ hoặc $\text{x - $\frac{1}{3}$}$ = $\frac{-1}{36}$
⇒ $\text{x = $\frac{13}{36}$}$ hoặc $\text{x = $\frac{11}{36}$}$
Vậy $\text{x = $\frac{13}{36}$}$ hoặc $\text{x = $\frac{11}{36}$}$
5, 4(2x - 1)² = 9
(2x - 1)² = $\frac{9}{4}$
⇒ 2x - 1 = $\frac{9}{4}$ hoặc 2x - 1 = $\frac{-9}{4}$
⇒ 2x = $\frac{13}{4}$ hoặc 2x = $\frac{-5}{4}$
Vậy 2x = $\frac{13}{4}$ hoặc 2x = $\frac{-5}{4}$
6, -2(3 - x)² = -72
(3 - x)² = (-72) : (-2)
(3 - x)² = 36
⇒ 3 - x = 6 hoặc 3 - x = -6
⇒ x = -3 hoặc x = 9
Vậy x = -3 hoặc x = 9
7, (-3x)³ = -125
⇒ -3x = -5
⇒ x = $\frac{5}{3}$
Vậy x = $\frac{5}{3}$
8, $\text{(x - $\frac{1}{3}$)}^{3}$ = $\frac{-8}{27}$
⇒ $\text{x - $\frac{1}{3}$}$ = $\frac{-2}{3}$
⇒ $\text{x = $\frac{-1}{3}$}$
Vậy $\text{x = $\frac{-1}{3}$}$
9, $\text{(x - $\frac{2}{15}$)}^{3}$ = $\frac{8}{125}$
⇒ $\text{x - $\frac{2}{15}$}$ = $\frac{2}{5}$
⇒ $\text{x = $\frac{8}{15}$}$
Vậy $\text{x = $\frac{8}{15}$}$
10, $\text{$3^{x}$ = 27}$
$\text{$3^{x}$ = $3^{3}$}$
⇒ x = 3
Vậy x = 3
11, $\text{$(-2)^{2x}$ = -8}$
$\text{$(-2)^{2x}$ = $(-2)^{3}$}$
⇒ 2x = 3
⇒ x = $\frac{3}{2}$
Vậy x = $\frac{3}{2}$
12, $(\frac{-5}{3})^{x}$ = -$\frac{125}{27}$
$(\frac{-5}{3})^{x}$ = $(\frac{-5}{3})^{3}$
⇒ x = 3
Vậy x = 3
13, $(\frac{-1}{3})^{2x-1}$ = $\frac{-1}{27}$
$(\frac{-1}{3})^{2x-1}$ = $(\frac{-1}{3})^{3}$
⇒ 2x - 1 = 3
⇒ 2x = 4
⇒ x = 2
Vậy x = 2
14, $\frac{2^{4-x}}{16^{5}}$ = $32^{5}$
$\frac{2^{4-x}}{16^{5}}$ = $\frac{512^{5}}{16^{5}}$
${2}^{4-x}$ = ${512}^{5}$
${2}^{4-x}$ = $(2^{9})^{5}$
${2}^{4-x}$ = ${2}^{45}$
⇒ 4 - x = 45
⇒ x = -41
16,$(-\frac{3}{4})^{3x-1}$ = -$\frac{27}{64}$
$(-\frac{3}{4})^{3x-1}$ = $(-\frac{3}{4})^{3}$
⇒ 3x - 1 = 3
⇒ 3x = 4
⇒ x = $\frac{4}{3}$
Vậy x = $\frac{4}{3}$
17, $(\frac{4}{5})^{2x+5}$ = $\frac{256}{625}$
$(\frac{4}{5})^{2x+5}$ = $(\frac{4}{5})^{4}$
⇒ 2x + 5 = 4
⇒ 2x = -1
⇒ x = $\frac{-1}{2}$
Vậy x = $\frac{-1}{2}$
18, $\frac{(x+3)^{5}}{(x+3)^{2}}$ = $\frac{64}{27}$
$(x+3)^{5-2}$ = $\frac{64}{27}$
$(x+3)^{3}$ = $(\frac{4}{3})^{3}$
⇒ x + 3 = $\frac{4}{3}$
⇒ x = $\frac{-5}{3}$
Vậy x = $\frac{-5}{3}$
19, $7.2^{x}$ = $2^{9}$ + $5.2^{8}$
$7.2^{x}$ = $2.2^{8}$ + $5.2^{8}$
$7.2^{x}$ = $(2+5).2^{8}$
$7.2^{x}$ = $7.2^{8}$
⇒ $2^{x}$ = $2^{8}$
⇒ x = 8
Vậy x = 8.
20, $9.5^{x}$ = $6.5^{8}$ + $3.5^{8}$
$9.5^{x}$ = $(6+3).5^{8}$
$9.5^{x}$ = $9.5^{8}$
⇒ $5^{x}$ = $5^{8}$
⇒ x = 8
Vậy x = 8.
