Giải hộ mình câu này với các bạnGiải hộ mình câu này với các bạn $c)~(2-3x)^2=\frac94$ $d)~(x+5)^3=-\frac{64}{125}$,$e)~(x-\frac56)^2=\frac1{36}$ $f)~(x-\frac18)^3=\frac{-8}{125}$,$g)~(3x-4)^2=(-\frac34)^2$ $h)~(\frac12)^x=(\frac1{32})^4$,$i)~(\frac{-2}3)^x=\frac{-8}{27}$ $k)~(\frac12)^{2x-1}=\frac18$,$l)~(\frac13)^{2x-1}=3^5$ $m)~18^x:3^x=216$,$n)~100^x:20^x=125^6$ $o)~36^{3x}:6^x=36^5$,$p)~3^x-3^{x+3}=-234$ $q)~(2x-\frac13)^2=(-\frac23)^4$

Question

Accepted Answer

{"userId":5292268,"userName":"Quỳnh Quỳnh"}

c)

(2 – 3x)² = 9/4

=> 2 – 3x = ±3/2

=> 3x = 2 ∓ 3/2

=> x = (2 ∓ 3/2)/3 = (1/6 hoặc 7/6)

d)

(x + 5)³ = –64/125

=> x + 5 = –4/5

=> x = –4/5 – 5 = –29/5

e)

(x – 5/6)² = 1/36

=> x – 5/6 = ±1/6

=> x = 5/6 ± 1/6 → x = 1 hoặc x = 2/3

f)

(x – 1/8)³ = –8/125

=> x – 1/8 = –2/5

=> x = –2/5 + 1/8 = –11/40

g)

(3x – 4)² = (–3/4)²

=> 3x – 4 = ±3/4

=> x = (4 ± 3/4)/3 = 19/12 hoặc 13/12

h)

(1/2)^x = (1/32)^4

=> (1/2)^x = 1/2⁵×⁴ = 1/2²⁰

=> x = 20

i)

(–2/3)^x = –8/27

=> (–2/3)^x = (–2/3)³

=> x = 3

k)

(1/2)^(2x – 1) = 1/8

=> (1/2)^(2x – 1) = (1/2)³

=> 2x – 1 = 3

=> x = 2

l)

(1/3)^(2x – 1) = 3⁵

=> (3⁻¹)^(2x – 1) = 3⁵

=> 3^–(2x – 1) = 3⁵

=> –(2x – 1) = 5

=> 2x – 1 = –5

=> x = –2

m)

18^x × 3^x = 216

=> (18 × 3)^x = 216 → 54^x = 216

=> thử x = 1: 54 → không

=> thử x = 2: 54² = 2916 → quá lớn

=> nhưng 18 = 2 × 3², 3 = 3, nên:

18^x × 3^x = (2 × 3²)^x × 3^x = 2^x × 3^3x

216 = 2³ × 3³

=> 2^x × 3^3x = 2³ × 3³

=> x = 1

n)

100^x : 20^x = 125⁶

=> (100 / 20)^x = 125⁶

=> (5)^x = 5⁶

=> x = 6

o)

36^(3x) : 6^x = 36⁵

=> 36^(3x)/6^x = 36⁵

=> viết lại 36 = 6²

=> (6²)^(3x)/6^x = (6²)^5

=> 6^(6x)/6^x = 6^10

=> 6^(5x) = 6^10

=> 5x = 10

=> x = 2

p)

3^x – 3^(x + 3) = –234

=> đặt a = 3^x → 3^(x + 3) = a × 27

=> a – 27a = –234

=> –26a = –234 → a = 9 → 3^x = 9 → x = 2

q)

(2x – 1/3)² = (–2/3)^4

=> (2x – 1/3)² = (4/9)

=> 2x – 1/3 = ±2/3

=> 2x = 1/3 ± 2/3 → x = 1 hoặc –1/6