\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}\left(5-3\right)=2.5^{11}\)

\(5^{x+3}.2=2.5^{11}\)

\(5^{x+3}=5^{11}\)

\(x+3=11\)

\(x=8\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(4^{x+1}.13=13.4^{11}\)

\(4^{x+1}=4^{11}\)

\(x+1=11\)

\(x=10\)

 a )  5^n = 125 

      5^n = 5^3 

         n = 3 

 b )      3^4 . 3^n = 3^7 

          3^(4 + n ) =3^7 

              4 + n   = 7 

                   n    = 7 - 4 

                  n    =   3

còn câu nx gips mk vs

Ta có :

\(5^n=125\)

\(\Leftrightarrow\)\(5^n=5^3\)

\(\Leftrightarrow\)\(n=3\)

Vậy \(n=3\)

Ta có :

\(3^4.3^n=3^7\)

\(\Leftrightarrow\)\(3^{n+4}=3^7\)

\(\Leftrightarrow\)\(n+4=7\)

\(\Leftrightarrow\)\(n=7-4\)

\(\Leftrightarrow\)\(n=3\)

Vậy \(n=3\)

Bài 3 :

a) 4.(x-5) - 2 ³=2⁴.3

4x-20-8=48

4x=76

x=19

b) 4.x³+15=271

4.x³=256

x³=64

=> x=4

c) ( 2x-3)²= 169

=> 2x-3= 13

2x=16

x=8

 Chúc bạn học tốt !

4*(x-5) - 2^3 = 2^4*3 

4*(x-5) - 8 = 16*3 

4*(x-5) - 8 = 48 

4*(x-5) = 48 + 8 

4*(x-5) = 56 

x- 5 = 56 : 4 

x - 5 = 14 

x = 14 + 5 

x = 19 

4*x^3 + 15 = 271 

4*x^3 = 271 - 15 

4*x^3 = 256 

x^3 = 256 : 4 

x^3 = 64 

x^3 = 4^3 

x = 4 

a) \(\Leftrightarrow2.\left(\frac{2.3^x}{3}+3^x.3^2\right)=2.3^6\left(2+3^3\right)\)

\(\Leftrightarrow2.\left(\frac{2.3^x+3.3^x.3^2}{3}\right)=2.3^6.29\)

\(\Leftrightarrow2.\left[\frac{3^x.\left(2+3.3^2\right)}{3}\right]=2.3^6.19\)

\(\Leftrightarrow2.3^{x-1}.29=2.3^6.29\Leftrightarrow3^{x-1}.29=\frac{2.3^6.29}{2}=3^6.29\Leftrightarrow3^{x-1}=\frac{3^6.29}{29}=3^6\)

\(\Leftrightarrow3^{x-1}=3^6\Leftrightarrow x-1=6\Leftrightarrow x=6+1=7\)

vậy x=7 . Chọn mình nha

mấy bài sao tương tự nếu ko biết thì nhắn tin mình chỉ típ nha

a, => 2^x = (2^3)^4/(2^4)^3 = 2^12/2^12 = 1 = 2^0

=> x = 0

c, => 4^x = 4^10.(4-3) = 4^10

=> x=10

d, => 2^2.3^x-1 + 2.3^x.9 = 2^2.3^6+2.3^9

=> 2.3^x-1 . (2+3.9) = 2.3^6.(2+3^3)

=> 2.3^x-1 . 27 = 2.3^6 . 27

=> 3^x-1 = 3^6

=> x-1 = 6

=> x = 7

e, => 2^x.(1/3+1/6+2) = 2^11.(2+1/2)

=> 2^x. 5/2 = 2^11. 5/2

=> 2^x = 2^11

=> x = 11

Tk mk nha

câu b) chưa có ai làm thì mình làm nốt vậy 

\(\left(-2\right)^2=-4^6-8^5\)

\(\left(-2\right)^x=-4096-32768\)

\(\left(-2\right)^x=-36864\)

\(\Rightarrow x\) sẽ 1 số thập phân nào đó 

a)\(\left(\frac{1}{2}-\frac{1}{3}\right).6^x+6^{x+2}=6^{15}+6^{18}\)

\(\frac{1}{6}.6^x+6^{x+2}=6^{15}\left(1+6^3\right)\)

\(\frac{1}{6}.6^x\left(1+6^3\right)=6^{15}.217\)

\(6^{x-1}.217=6^{15}.217\)

\(6^{x-1}=6^{15}\)

\(x-1=15\)

\(x=16\)

b) \(\left(\frac{1}{2}-\frac{1}{6}\right).3^{x+4}-4.3^x=3^{16}-4.3^{13}\)

\(\frac{1}{3}.3^x.4\left(3^4-1\right)=3^{13}.4\left(3^3-1\right)\)

\(3^x.4.\left(3^3-1\right)=3^{13}.4.\left(3^3-1\right)\)

\(3^x=3^{13}\)

\(x=13\)

\(\left(\frac{1}{2}-\frac{1}{6}\right).\left(3^x.3^4\right)-4.3^x=3^{16}-4.3^{13}\)

=> \(\frac{1}{3}.3^x.3^4-4.3^x=3^{16}-4.3^{13}\)

=> \(3^x.3^4-4.3^x=\left(3^{16}-4.3^{13}\right):\frac{1}{3}\)

=> \(3^x.3^4-4.3^x=-386339074,3\)

=> \(3^x.\left(3^4-4\right)=-386339074,3\)

=> \(3^x.77=-386339074,3\)

=> \(3^x=-386339074,3:77\)

=> \(3^x=-5017390,575\)

=> x = ... chắc tự ngồi tính đc

cái a tương tự thôi

a) 1440: [41-{2x-5}]=16.3

    41-(2x-5)=1440-48

   41-(2x-5)=1392

     2x-5=41-1392

     2x-5=-1351

        2x=-1351+5

        2x=-1346

         x=(-1346):2

         x=-673

b) 5.[225-(x-10)]-125=0

      5.[225-(x-10)=0+125

          225-(x-10)=125:5

          225-(x-10)=25

                x-10=225-25

               x-10=200

               x=200+10

             x=210

c) x thuộc {1,2,3,6}