a, \(\left(2x+7\right)^4=10^{11}:10^7\)

\(\Rightarrow\left(2x+7\right)^4=10^4\)

\(\Rightarrow2x+7=10\)

\(\Rightarrow2x=10-7\)

\(\Rightarrow2x=3\)

\(\Rightarrow x=\dfrac{3}{2}\) hay \(x=1,5\)

b, \(5^{x-1}.7^{x-1}=25.49\)

\(\Rightarrow\)\(5^{x-1}.7^{x-1}=5^2.7^2\)

\(\Rightarrow\left\{{}\begin{matrix}5^{x-1}=5^2\\7^{x-1}=7^2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x-1=2\\x-1=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=3\\x=3\end{matrix}\right.\)

c, \(\left(x-5\right)^{2018}=9.\left(x-5\right)^{2016}\)

\(\Rightarrow\dfrac{\left(x-5\right)^{2018}}{\left(x-5\right)^{2016}}=9.\dfrac{\left(x-5\right)^{2016}}{\left(x-5\right)^{2016}}\)

\(\Rightarrow\left(x-5\right)^2=9\)

\(\Leftrightarrow\left(x-5\right)^2=3^2\)

\(\Rightarrow x-5=3\)

\(\Rightarrow x=3+5\)

\(\Rightarrow x=8\)

55⁵ x 55¹⁰ = 55¹⁵

6666¹² x 6666¹⁰ = 6666²²

5¹⁰ x 5¹ = 5¹¹

22¹ x 22¹⁰ = 22¹¹

10¹ x 10² = 10¹²

55⁵x55¹⁰=55¹⁵

6666¹²x6666¹⁰=6666²²

5¹⁰x5¹=5¹¹

22¹x 22¹⁰=22¹¹

10¹x10²=10³

1. Tính:

B= 12 . 108+ 17 . 107

B = 1296 + 1819

B = 3115

2. Tìm x:

a) 4x = 2x+1

4x - 2x = 1

2x = 1

x = 1/2

Vậy x = 1/2

b) 16 = (x-1)^4

2^4 = (x - 1)^4

x - 1 = - 2 hoặc x - 1 = 2

x - 1 = -2, x = -2 + 1, x = -1

x - 1 = 2, x = 2 + 1, x = 3

Vậy x ∈ {-1; 3}

2.

\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)

4^2x-6 = 1

=> 4^2x-6 = 4⁰

=> 2x - 6 = 0

=> 2x = 6

=> x=3

xrnthftyhbt76uyt

3 phần trên đễ quá mik ko làm mik chỉ làm phàn 4 thôi nhé

4)  ta có: (x-3)^x+2=(x-3)^x+6

=>(x-3)^x*(x-3)^2=(x-3)^x*(x-3)^6

=>(x-3)^x=(x-3)^x*(x-3)^4

=>(x-3)^x*(x-3)^4-(x-3)^x*1=0

=>(x-3)^x*((x-3)^4-1)=0

=>(x-3)^x=0 hoặc (x-3)^4-1=0

còn lại cậu tự làm nha nó đẽ mà

1)71.2-6(2.x+5)=10⁵:10³

   71.2-6(2.x+5)=10²

           6(2.x+5)=142-100

           6(2.x+5)=42

              2.x+5 =42:6

              2x+5  =7

              2x      =7-5

             2x       =2

              x        =1

2)5³.(3.x+2):13=10³:(13⁵:13⁴)

   5³.(3x+2):13 =10³:13

      5³(3x+2)    =10³

   125(3x+2)    =1000

          3x+5     =1000:125

          3x+5     =8

          3x          =8-5

          3x          =3

            x          =3:3

           x           =1

Quy ước toán học dấu x = dấu .

===================================

1. (3^x - 5)⁴ = 2⁸

<=> (3^x - 5)⁴ = 4⁴

=> Ta có 2 trường hợp :

* TH1 : \(3^x-5=4\Rightarrow3^x=9\Rightarrow x=2\)

* TH2 : \(3^x-5=-4\Rightarrow3^x=1\Rightarrow x=0\)

Vậy x=1 hoặc x=0

a, \(\left(3^x-5\right)^4=2^8\)

\(\Rightarrow\left(3^x-5\right)^4=\left(2^2\right)^4\)

\(\Rightarrow\left(3^x-5\right)^4=4^4\)

\(\Rightarrow3^x-5=4\Rightarrow3^x=1=3^0\)

\(\Rightarrow x=0\)

b, \(3^{x+2}+3^x=10^2-10\)

\(\Rightarrow3^x.\left(3^2+1\right)=100-10\)

\(\Rightarrow3^x.10=90\Rightarrow3^x=9=3^2\)

\(\Rightarrow x=2\)

c, \(3^{x+1}-3^x=4.5-2\)

\(\Rightarrow3^x.\left(3-1\right)=20-2\)

\(\Rightarrow3^x.2=18\Rightarrow3^x=9=3^2\)

\(\Rightarrow x=2\)

Chúc bạn học tốt!!! Mấy câu còn lại làm tương tự!

x^10=1=>x=1

x^10=N

x=3