a/2.5^x+1+10=60

2.5^x+1=50

5^x+1=25

5^x+1=5⁵

x+1=5

x=6

b/(x-1)²=4

(x-1)²=2² hoặc (x-1)² = (-2)²

x-1=2 hoặc x-1=-2

x=3 hoặc x=-1

c/ (2x+1)²=25

 (2x+1)²=5² hoặc (2x+1)²=(-5)² 

2x+1=5 hoặc 2x+1 = -5

2x=4 hoặc 2x=-6

x=2 hoặc x=-3

câu d hình như đề sai

a)2.5^x+1+10=60    ➩2.5^x+1=60-10=50    ➩5^x+1=50:2=25    ➩5^x+1=5² ➩x+1=2    ➩x=1

b)(x-1)²=4   ➩x-1=2  hoặc  x-1=-2      ➩x=3 hoặc x=-1

    *phần b,c mình ghi "hoặc" thì bạn dùng dấu ngoặc vuông nhé *                 

C)(2x+1)²=25.   ➩(2x+1)²=5²        ➩2x+1=5 hoặc 2x+1=-5 

➩x=2 hoặc x=-3

Phần D là 2^x+2^x+3=144 hay 2^x+2^x+3 =144 thế

\(a,2^x+2^{x+3}=144\\ 2^x.\left(1+2^3\right)=144\\ 2^x.9=144\\ 2^x=144:9\\ 2^x=16=2^4\\ vậy:x=4\)

\(b,\left(x-5\right)^{2022}=\left(x-5\right)^{2021}\\ Vì:\left[{}\begin{matrix}0^{2022}=0^{2021}\\1^{2022}=1^{2021}\end{matrix}\right.\\ Vậy:\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

\(c,\\ \left(2x+1\right)^3=9.81\\ \left(2x+1\right)^3=3^2.3^4\\ \left(2x+1\right)^3=3^6\\ \left(2x+1\right)^3=\left(3^2\right)^3=9^3\\ Vậy:2x+1=9\\ 2x=9-1\\ 2x=8\\ x=\dfrac{8}{2}\\ x=4\)

Tham khảo:Tìm x thuộc N , biết:a)  2x + 2x+3  =144b) (4x -1)2 =25 x 9  - Hoc24

Ta có: 2x + 2x + 3 = 144

=> 2x + 2x.23 = 144

=> 2x.(1 + 8) = 144

=> 2x.9 = 144

=> 2x = 144 : 9 = 16 = 24

=> x = 4.

Vậy x= 4

x= 4

\(a,2^{x+1}=32\\ 2^{x+1}=2^5\\ x+1=5\\ x=4\\ b,2^{2x}+2^{2x+1}=48\\ 2^{2x}+2\cdot2^{2x}=48\\ 3\cdot2^{2x}=48\\ 2^{2x}=16\\ 2^{2x}=2^4\\ 2x=4\\ x=2\)

\(c,3^x+5\cdot3^{x+1}=144\\ 3^x+15\cdot3^x=144\\ 16\cdot3^x=144\\ 3^x=9\\ 3^x=3^2\\ x=2\\ d,3^{x+5}=9^{x+1}\\ 3^{x+5}=3^{2x+2}\\ x+5=2x+2\\ x=3\)

a: \(\Leftrightarrow2^{2x}\cdot8+2^{2x}\cdot2+2^{2x}=176\)

\(\Leftrightarrow2^{2x}=16\)

=>2x=4

=>x=2

b: \(\Leftrightarrow2^{2x}\left(2^3+2-1\right)=144\)

\(\Leftrightarrow2^{2x}=16\)

=>2x=4

=>x=2

a) \(\left(x-\dfrac{1}{4}\right)^2=\dfrac{4}{9}\)

\(\left(x-\dfrac{1}{4}\right)^2=\left(\dfrac{2}{3}\right)^2\)

\(x-\dfrac{1}{4}=\dfrac{2}{3}\)

\(x=\dfrac{2}{3}+\dfrac{1}{4}\)

\(x=\dfrac{8}{12}+\dfrac{3}{12}\)

\(x=\dfrac{11}{12}\)

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