Ta có: \(4.3^{x+2}-2.3^{x+1}=810\)

\(4.3^{x+1}.3-2.3^{x+1}=810\)

\(2.3^{x+1}\left(2.3-1\right)=810\)

\(2.3^{x+1}.5=810\)

\(3^{x+1}=81=3^4\)

x+1=4

x=3

\(3^{x+2}+4\cdot3^{x+1}=7\cdot3^6\\ 3^x\cdot3^2+4\cdot3^x\cdot3=5103\\ 3^x\left(9+12\right)=5103\\ 3^x\cdot21=5103\\ 3^x=243\\ 3^x=3^5\\ x=5\)

\(4\cdot3^{x+2}-3^{x-1}=963\\ \Leftrightarrow36\cdot3^x-\dfrac{1}{3}\cdot3^x=963\\ \Leftrightarrow3^x=27\\ \Leftrightarrow x=3\)

\(4.3^{x+2}-3^{x-1}=963\\ \Leftrightarrow4.3^2.3^x-\dfrac{3^x}{3}=963\\ \Leftrightarrow3^x.\left(36-\dfrac{1}{3}\right)=963\\ \Leftrightarrow3^x.\dfrac{107}{3}=963\\ \Leftrightarrow3^x=27\\ \Leftrightarrow3^x=3^3\\ \Leftrightarrow x=3\)

Vậy x= 3

Đáp án A

Chọn A

a ) 9 . 3x = 81

          3x = 9

            x = 3

b ) 2x : 4 = 1

     2x      = 4

       x      = 2

c ) 2x - 64 = 2

     2x        = 66

       x        = 33

d ) 2x = 16

       x  = 8

e ) 3 ^ 2 . 3 ^ 4 . 3x = 3 ^ 10

     3 ^ ( 2 + 4 + x )  = 3 ^ 10

=> 2 + 4 + x = 10

                 x = 4

f ) 2x + 4 . 2x = 5 . 2 ^ 5

    2x + 8 x     = 160

    10x            = 160

        x            = 16

\(a.9.3x=81\)

\(3x=81:9\)

\(3x=9\)

\(x=9:3\)

\(x=3\)

a: =>\(4\cdot3^x\cdot\dfrac{1}{3}+2\cdot3^x\cdot9=4\cdot3^6+2\cdot3^9\)
=>3^x(4*1/3+2*9)=3^6(4+2*3^3)

=>3^x*58/3=3^6*58

=>3^x/3^6=3

=>x-6=1

=>x=7

b: =>\(2^x\cdot\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)=2^7\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)\)

=>2^x=2^7

=>x=7

Đặt \(3^x=a\)  \(\left(a>0\right)\)

Phương trình \(\Leftrightarrow a^2-4a+m-2=0\) (*)

Yêu cầu bài toán \(\Leftrightarrow\) Phương trình (*) có 2 nghiệm dương phân biệt

\(\Leftrightarrow\left\{{}\begin{matrix}\Delta'>0\\a_1+a_2>0\\a_1\cdot a_2>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}4-\left(m-2\right)>0\\4>0\left(t/m\right)\\m-2>0\end{matrix}\right.\) \(\Leftrightarrow\) ...