Bài 1:

a) \(4^{x+2}+4^x=68\)

\(\Rightarrow4^x\cdot\left(4^2+1\right)=68\)

\(\Rightarrow4^x\cdot17=68\)

\(\Rightarrow4^x=\dfrac{68}{17}\)

\(\Rightarrow4^x=4\)

\(\Rightarrow4^x=4^1\)

\(\Rightarrow x=1\)

b) \(5\cdot2^{x+4}-3\cdot2^x=308\)

\(\Rightarrow2^x\cdot\left(5\cdot2^4-3\right)=308\)

\(\Rightarrow2^x\cdot\left(5\cdot16-3\right)=308\)

\(\Rightarrow2^x\cdot77=308\)

\(\Rightarrow2^x=\dfrac{308}{77}\)

\(\Rightarrow2^x=4\)

\(\Rightarrow2^x=2^2\)

\(\Rightarrow x=2\)

c) \(4\cdot3^{x+1}+7\cdot3^x=513\)

\(\Rightarrow3^x\cdot\left(4\cdot3+7\right)=513\)

\(\Rightarrow3^x\cdot19=513\)

\(\Rightarrow3^x=\dfrac{513}{19}\)

\(\Rightarrow3^x=27\)

\(\Rightarrow3^x=3^3\)

\(\Rightarrow x=3\)

d) \(5^{x+4}-5^x=3120\)

\(\Rightarrow5^x\cdot\left(5^4-1\right)=3120\)

\(\Rightarrow5^x\cdot\left(625-1\right)=3120\)

\(\Rightarrow5^x\cdot624=3120\)

\(\Rightarrow5^x\cdot\dfrac{3120}{624}\)

\(\Rightarrow5^x=5\)

\(\Rightarrow5^x=5^1\)

\(\Rightarrow x=1\)

f) \(3\cdot4^{2x+1}-16^x=2816\)

\(\Rightarrow3\cdot4^{2x+1}-\left(4^2\right)^x=2816\)

\(\Rightarrow3\cdot4^{2x+1}-4^{2x}=2816\)

\(\Rightarrow4^{2x}\cdot\left(3\cdot4-1\right)=2816\)

\(\Rightarrow4^{2x}\cdot11=2816\)

\(\Rightarrow4^{2x}=\dfrac{2816}{11}\)

\(\Rightarrow4^{2x}=256\)

\(\Rightarrow\left(2^2\right)^{2x}=2^8\)

\(\Rightarrow2^{4x}=2^8\)

\(\Rightarrow4x=8\)

\(\Rightarrow x=2\)

Bài 2:

\(2^x+124=5^y\)

\(\Rightarrow5^y-2^x=124\)

\(\Rightarrow5^y-2^x=125-1\)

\(\Rightarrow\left\{{}\begin{matrix}5^y=125\\2^x=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}5^y=5^3\\2^x=2^0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}y=3\\x=0\end{matrix}\right.\)

Vậy: .... 

8^x=2¹¹¹

=>(2³)^x=2¹¹¹

=>2^3x=2¹¹¹

=>3x=111

=>x=37

2^x+5.2^x=48

=>2^x.6=48

=>2^x=8=2³

=>x=3

Câu cuối ko làm đc nha

a. 8^x = 2¹¹¹

    2^3x = 2¹¹¹

    3x  = 111

      x  = 111:3

     x  = 37

b. 2^x + 5.2^x = 48

    2^x(5 + 1 )= 48

    2^x.6        = 48

    2^x           = 48 : 6

    2^x           = 8

    2^x            = 2³

      x            = 3

c. 2^x + 3.2^x-1 = 40

   2^x(3:2 +1 )     = 40

   2^x . \(\frac{5}{2}\)      = 40

    2^x                  = 40 : \(\frac{5}{2}\)

    2^x                  = 16

    2^x                   = 2⁴

      x                   = 4

+) \(8^x=2^{111}\)

\(\Rightarrow\left(2^3\right)^x=2^{111}\)

\(\Rightarrow2^{3x}=2^{111}\)

\(\Rightarrow3x=111\)

\(\Rightarrow x=111:3\)

\(\Rightarrow x=37\)

Vậy x = 37

+) \(2^x+5\times2^x=48\)

\(\Rightarrow2^x\times\left(1+5\right)=48\)

\(\Rightarrow2^x\times6=48\)

\(\Rightarrow2^x=48:6\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

Vậy x = 3

+) \(2^x+3\times2^{x-1}=40\)

\(\Rightarrow2^x+3\times2^x:2=40\)

\(\Rightarrow2^x+3\times2^x\times\frac{1}{2}=40\)

\(\Rightarrow2^x+2^x\times\left(3\times\frac{1}{2}\right)=40\)

\(\Rightarrow2^x+2^x\times\frac{3}{2}=40\)

\(\Rightarrow2^x\times\left(1+\frac{3}{2}\right)=40\)

\(\Rightarrow2^x\times\frac{5}{2}=40\)

\(\Rightarrow2^x=40:\frac{5}{2}\)

\(\Rightarrow2^x=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

Vậy x = 4

_Chúc bạn học tốt_

may cai bai day ma cung khong biet oc cho

a) 89-(73-x)=20

=>73-x=89-20

=>73-x=69

=>x=73-69

=>x=4

Dài quá bn ơi, vs lại mấy cái này cx ko khó lắm đâu (nếu ko lm đc đăng mỗi lần một ít thui chứ dài quá mk đọc cn lười chứ đừng ns là làm)

a: =>x-8=27

hay x=35

3.(x-8) = 106-25

3.(x-8) = 81

x-8 = 81:3

x-8 = 27

x=35

\(a,25+3\left(x-8\right)=106\\ 3\left(x-8\right)=81\\ x-8=27\\ x=35\)

3² . (x + 4 ) - 5² = 5 . 2²

9  . ( x + 4 ) - 25 = 20

9 . ( x + 4 )        = 20 + 25

9 . ( x + 4 )        = 45

     ( x + 4 )       = 45 : 9

      x  + 4          = 5

      x                 = 5 - 4

      x                 = 1

đây nè mấy nàng ơi. trả lời câu này nhé . làm ơn đi