`#3107`

b)

`2.3^x = 162`

`\Rightarrow 3^x = 162 \div 2`

`\Rightarrow 3^x = 81`

`\Rightarrow 3^x = 3^4`

`\Rightarrow x = 4`

Vậy, `x = 4`

c)

`(2x - 15)^5 = (2 - 15)^3`

\(\Rightarrow \)`(2x - 15)^5 - (2x - 15)^3 = 0`

\(\Rightarrow \)`(2x - 15)^3 . [ (2x - 15)^2 - 1] = 0`

\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=15\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x-15=1\\2x-15=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x=16\\2x=-14\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=-7\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)

`d)`

\(3^{x+2}-5.3^x=?\) Bạn ghi tiếp đề nhé!

`e)`

\(7\cdot4^{x-1}+4^{x-1}=23?\)

\(4^{x-1}\cdot\left(7+1\right)=23\\ \Rightarrow4^{x-1}\cdot8=23\\ \Rightarrow4^{x-1}=\dfrac{23}{8}\)

Bạn xem lại đề!

`f)`

\(2\cdot2^{2x}+4^3\cdot4^x=1056\)

\(\Rightarrow2\cdot2^{2x}+\left(2^2\right)^3\cdot\left(2^2\right)^x=1056\\ \Rightarrow2\cdot2^{2x}+2^6\cdot2^{2x}=1056\\ \Rightarrow2^{2x}\cdot\left(2+2^6\right)=1056\\ \Rightarrow2^{2x}\cdot66=1056\\ \Rightarrow2^{2x}=1056\div66\\ \Rightarrow2^{2x}=16\\ \Rightarrow2^{2x}=2^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)

Vậy, `x = 2`

_____

\(10 -{[(x \div 3+17) \div 10+3.2^4] \div 10}=5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)

\(\Rightarrow\left(x\div3+17\right)\div10+48=50\)

\(\Rightarrow\left(x\div3+17\right)\div10=2\)

\(\Rightarrow x\div3+17=20\)

\(\Rightarrow x\div3=3\\ \Rightarrow x=9\)

Vậy, `x = 9.`

1.

a) ( x - 140) : 7 = 3³ - 2³ x 3

=>( x - 140) : 7 = 27 - 8 x 3

    ( x - 140) :7  = 27 - 24

    ( x - 140) : 7 = 3

     x - 140         = 3 x 7

     x - 140         = 21

            x           = 21 + 140

            x           = 161 

b) 2^x : 2⁵ = 1

    2^{x - 5}    = 1

=>2^{x - 5}    = 2⁰

=> x - 5    = 0

        x       = 0 + 5

        x       = 5

\(\Leftrightarrow3^{x-1}\left(1+5\right)=162\)

\(\Leftrightarrow3^{x-1}.6=162\)

\(\Leftrightarrow3^{x-1}=27\)

\(\Leftrightarrow x-1=3\)

\(\Leftrightarrow x=3+1=4\)

\(3^{x-1}+5.3^{x-1}=162\)

\(3^{x-1}.\left(1+5\right)=162\)

\(3^{x-1}.6=162\)

\(3^{x-1}=27\)

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

\(\Leftrightarrow x-1=3\)
       \(x=4\)

Vậy x = 4

\(3^{x-1}\)+5.\(3^{x-1}\)=162

\(\Rightarrow\)\(3^{x-1}\).(1+5)=162

\(\Rightarrow\)\(3^{x-1}\).6=162

\(\Rightarrow\)\(3^{x-1}\)=27

\(\Rightarrow\)\(3^x\):3=27

\(\Rightarrow\)\(3^x\)=\(3^2\)

\(\Rightarrow\)x=2

vậy x=2

a)3^x-1+5.3^x-1=162

3^x-1.1+5.3^x-1=162

3^x-1.(5+1)=162

3^x-1.6=162

3^x-1=162/6

3^x-1=27

3^x-1=3³ 

Suy ra x-1=3

x=3+1=4

b)2^x+3+2^x=144

2^x.8+2^x=144

2^x.8+2^x.1=144

2^x.(8+1)=144

2^x.9=144

2^x=144/9

2^x=16

2^x=2⁴

Suy ra x=4