`#3107.101107`

a)

\(5\left(x-1\right)^3=40\\\Rightarrow\left(x-1\right)^3=40\div5\\ \Rightarrow\left(x-1\right)^3=8\\ \Rightarrow\left(x-1\right)^3=2^3\\ \Rightarrow x-1=2\\ \Rightarrow x=2+1\\ \Rightarrow x=3\)

Vậy, `x = 3`

b)

\(3^{2x+1}+9^x=324?\\ \Rightarrow3^{2x}\cdot3+3^{2x}=324\\ \Rightarrow3^{2x}\cdot\left(3+1\right)=324\\ \Rightarrow3^{2x}\cdot4=324\\ \Rightarrow3^{2x}=81\\ \Rightarrow3^{2x}=3^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)

Vậy, `x = 2`

c)

\(5^x-13=3\cdot2^2\\ \Rightarrow5^x-13=12\\ \Rightarrow5^x=12+13\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)

Vậy, `x = 2`

d)

\(8^x+2^{3x+1}=192\\ \Rightarrow2^{3x}+2^{3x}\cdot2=192\\ \Rightarrow2^{3x}\left(1+2\right)=192\\ \Rightarrow2^{3x}\cdot3=192\\ \Rightarrow2^{3x}=64\\ \Rightarrow2^{3x}=2^6\\ \Rightarrow3x=6\\ \Rightarrow x=2\)

Vậy, `x = 2.`

a) 3^2x + 3^2x+1 = 324

3^2x . 1 + 3^2x . 3 = 324

3^2x . ( 1 + 3 ) = 324

3^2x . 4 = 324

3^2x = 324 : 4

3^2x = 81

3^2x = 3⁴

=> 2x = 4

=> x = 4 : 2 = 2

( 3x - 7 )²⁰¹² = ( 3x - 7 )²⁰¹⁴

( 3x - 7 )²⁰¹⁴ - ( 3x - 7 )²⁰¹² = 0

( 3x - 7 )²⁰¹² . [ ( 3x - 7 )² - 1 ] = 0

\(\Rightarrow\orbr{\begin{cases}\left(3x-7\right)^{2012}=0\\\left(3x-7\right)^2-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x-7=0\\\left(3x-7\right)^2=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=7\\3x-7=1\text{ hoặc }3x-7=-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{7}{3}\\3x=8\text{ hoặc }3x=6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x=\frac{8}{3}\text{ hoặc }x=2\end{cases}}\)

1b) có thiếu ko cau?

`1a)5^3` và `3^5`

`5^3=125`

`3^5=243`

Vì `243>125` nên `3^5>5^3`

__

`c)3^24` và `27^7`

`27^7=(3^3)^7=3^21`

Vì `3^24>3^31` nên `3^24>27^7`

`2a)x^3=216`

`=>x^3=6^3`

`=>x=6`

__

`b)3^x+15=18`

`=>3^x=18-15`

`=>3^x=3`

`=>x=1`

324-3x=270:15

=>324-3x=18

=>3x=324-18

=>3x=306

=>x=306:3=102

+) \(24+\left(x-6\right)=135\)

\(\Rightarrow x-6=135-24=111\)

\(\Rightarrow x=111+6=117\)

+) \(2019-2\cdot\left(3x-2\right)=19\)

\(\Rightarrow2\cdot\left(3x-2\right)=2019-19=2000\)

\(\Rightarrow3x-2=2000:2=1000\)

\(\Rightarrow3x=1000+2=1002\)

\(\Rightarrow x=1002:3\)

\(\Rightarrow x=334\)

+) \(3^x+3^{x+1}=324\)

\(\Rightarrow3^x+3^x\cdot3=324\)

\(\Rightarrow3^x\cdot\left(1+3\right)=324\)

\(\Rightarrow3^x\cdot4=324\)                      \(\Rightarrow3^x=324:4=81\)

\(\Rightarrow3^x=3^4\)                           \(\Rightarrow x=4\)

3x + 3x + 1 = 324

  (3 + 3 ). x = 324 - 1

            6x  = 323

              x  = 323 : 6

              x = \(\frac{323}{6}\)= \(53\frac{5}{6}\)

có 3x+3x+1=324

=>3x+3x=324-1

=>3x+3x=323

=>2.3x=323

=>6x=323

=>x=\(\frac{323}{6}\)

3x + 3x + 1 = 324

3x + 3x = 323

6x = 323

x = 323 : 6

x = 323

0,36 x 550 + 0,18 x 126 x 2 + 3 x 324 x 0,12

= 0,36 x 550 + 0,18 x 2 x 126 + 3 x 0,12 x  324

= 0,36 x 550 + 0,36 x 126 + 0,36 x 324

= 0,36 x ( 550 + 126 + 324 )

= 0,36 x 1000

= 360

Ta có : 0,36 x 550 + 0,18 x 126 x 2 + 3 x 324 x 0,12

         = 0,36 x 550 + 0,36 x 126 + 0,36 x 324

        =   0,36 x ( 550 + 126 + 324 )

        =  0,36  x          950

        =        162

0,36x550+0,,18x126x2+3x324x0,12=0,36x550+0,36x126+0,36x324

                                                    =0,36x(550+126+324)

                                                    =0,36x1000=360

\(3^x\cdot4=324\)
\(\Leftrightarrow3^x=\dfrac{324}{4}=81\)
\(\Leftrightarrow3^x=3^4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)

\(3^x\cdot4=324\)

\(\Rightarrow3^x=324:4\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

3 mũ 4 . 4 = 324