`#3107.\text {DN}`

\(3^{x+2}+4\cdot3^{x+1}+3^{x-1}=6^6\)

`=> 3^x*3^2 + 4*3^x*3 + 3^x * 1/3 = 6^6`

`=>3^x*(3^2 + 12 + 1/3) = 6^6`

`=> 3^x * 64/3 = 6^6`

`=> 3^x = 6^6 \div 64/3`

`=> 3^x = 2187`

`=> 3^x = 3^7`

`=> x = 7`

Vậy, `x = 7.`

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

3^x+2 + 4.3^x+1 = 7.3⁶

3^x+1.(3 + 4) = 7.3⁶

3^x+1.7 = 7.3⁶

=> 3^x+1 = 3⁶

=> x + 1 = 6

=> x = 5

Ta có 3^(x+2) +4.3^(x+1) +3^(x-1) =6^6

     => 3^x . 3^2 + 4.3^x.3+ 3^x.1/3 = 46656

     => 3^x( 9+12+1/3) =46656

     => 3^x .64/3 =46656

     => 3^x =2187

      =>3^x = 3^7

    => x=7

Vậy x=7

\(3^{x+2}+4.3^{x+1}+3^{x-1}=6^6\)

\(\Rightarrow3^{x-1}\left(3^3+4.3^2+1\right)=3^6.2^6\)

\(\Rightarrow3^{x-1}.64=3^6.64\)

\(\Rightarrow3^{x-1}=3^6\)

\(\Rightarrow x-1=6\Leftrightarrow x=7\)

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

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

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

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

\(x+3=11\)

\(x=8\)

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

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

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

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

\(x+1=11\)

\(x=10\)

a, \(\left(\frac{1}{2}-\frac{1}{3}\right)\cdot6^x+6^{x+2}=6^{10}+6^7\)

\(\Leftrightarrow\frac{1}{6}\cdot6^x+6^x\cdot6^2=6^{10}+6^7\)

\(\Leftrightarrow6^{x-1}\left(1+6^3\right)=6^7\left(6^3+1\right)\)

\(\Leftrightarrow6^{x-1}=6^7\Leftrightarrow x-1=7\)

\(\Leftrightarrow x=8\)

b, \(\left(\frac{1}{2}-\frac{1}{6}\right)\cdot3^{x+4}-4\cdot3^x=3^{16}-4\cdot3^{13}\)

\(\Leftrightarrow\frac{1}{3}\cdot3^{x+4}-4\cdot3^x=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x\cdot3^3-4\cdot3^x=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x\left(3^3-4\right)=3^{13}\left(3^3-4\right)\)

\(\Leftrightarrow3^x=3^{13}\Leftrightarrow x=13\)

a. x=8

b. x=13

còn cách tính thì mình quên rồi vì minh học cái này lâu lắm rồi ko nhớ đc.