a) x = 0

b) x = -1

c) x = -9

d) x = 24

e) x = 2 hoặc x = -4

f) x = 5 hoặc x = -3

Lời giải:

$x^2=4.4.4.4=16.16=(-16)(-16)=16^2=(-16)^2$

$\Rightarrow x=16$ hoặc $x=-16$.

a) \(8x+56:14=60\)

\(\Rightarrow8x+4=60\)

\(\Rightarrow8x=56\)

\(\Rightarrow x=\dfrac{56}{8}\)

\(\Rightarrow x=7\)

b) Mình làm rồi nhé !

c) \(41-2^{x+1}=9\)

\(\Rightarrow2^{x+1}=41-9\)

\(\Rightarrow2^{x+1}=32\)

\(\Rightarrow2^{x+1}=2^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=4\)

d) \(3^{2x-4}-x^0=8\)

\(\Rightarrow3^{2x-4}-1=8\)

\(\Rightarrow3^{2x-4}=9\)

\(\Rightarrow3^{2x-4}=3^2\)

\(\Rightarrow2x-4=2\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=3\)

g) \(65-4^{x+2}=2014^0\)

\(\Rightarrow65-4^{x+2}=1\)

\(\Rightarrow4^{x+2}=64\)

\(\Rightarrow4^{x+2}=4^3\)

\(\Rightarrow x+2=3\)

\(\Rightarrow x=1\)

i) \(120+2\left(4x-17\right)=214\)

\(\Rightarrow2\left(4x-17\right)=214-120\)

\(\Rightarrow2\left(4x-17\right)=94\)

\(\Rightarrow4x-17=47\)

\(\Rightarrow4x=47+17\)

\(\Rightarrow4x=64\)

\(\Rightarrow x=16\)

a: \(8x+56:14=60\)

=>8x+4=60

=>8x=60-4=56

=>x=56/8=7

b: \(5^{2x-3}-2\cdot5^2=5^2\cdot3\)

=>\(5^{2x-3}=5^2\cdot3+2\cdot5^2=5^3\)

=>2x-3=3

=>2x=6

=>x=3

c: \(41-2^{x+1}=9\)

=>\(2^{x+1}=41-9=32\)

=>x+1=5

=>x=4

d: \(3^{2x-4}-x^0=8\)

=>\(3^{2x-4}-1=8\)

=>\(3^{2x-4}=8+1=9\)

=>2x-4=2

=>2x=6

=>x=3

g: \(65-4^{x+2}=2014^0\)

=>\(65-4^{x+2}=1\)

=>\(4^{x+2}=65-1=64\)

=>x+2=3

=>x=1

i: 120+2(4x-17)=214

=>2(4x-17)=214-120=94

=>4x-17=94/2=47

=>4x=64

=>\(x=\dfrac{64}{4}=16\)

a) 2.3^x+2 + 4.3^x+1 = 10.3²⁰¹⁹

<=> 3^x+1(6 + 4) = 10.3²⁰¹⁹

<=> 10.3^x+1 = 10.3²⁰¹⁹

<=> 3^x+1 = 3²⁰¹⁹ 

<=> x = 2018.

b) (9-4x)³ = 125 = 5³

<=> 9 - 4x = 5

<=> 4 = 4x

<=> x = 1

c) 2.2².2³....2^x = 1024 = 2¹⁰

<=> 2^{(1+2+3+...+x)} = 2¹⁰

<=> 1+2+3+...+x = 10

<=>x.(x+1)/2 = 10

<=> x(x+1) = 20 = 4.5

<=> x = 4.

\(a,\Rightarrow\left(4x-1\right)^2=25=5^2=\left(-5\right)^2\\ \Rightarrow\left[{}\begin{matrix}4x-1=5\\4x-1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\\ b,\Rightarrow2^x\left(1+2^3\right)=144\\ \Rightarrow2^x=144:9=16=2^4\Rightarrow x=4\\ c,\Rightarrow3^{2x+3}=3^{2\left(x+3\right)}\\ \Rightarrow2x+3=2x+6\Rightarrow0x=3\left(vô.lí\right)\\ \Rightarrow x\in\varnothing\)

\(\Rightarrow\frac{3}{4}x-\frac{1}{4}=2x-6+\frac{1}{4}x\)

\(\Rightarrow\frac{3}{4}x-2x-\frac{1}{4}x=-6+\frac{1}{4}\)

\(\Rightarrow-\frac{3}{2}x=-\frac{23}{4}\)

\(\Rightarrow x=\frac{23}{4}:\frac{3}{2}=\frac{23}{6}\)

\(\Rightarrow\frac{8}{9}x-\frac{1}{3}x=\frac{2}{3}+\frac{11}{3}\)

\(\Rightarrow\frac{5}{9}x=\frac{13}{3}\)

\(\Rightarrow x=\frac{13}{3}:\frac{5}{9}=\frac{39}{5}\)

\(\Rightarrow\frac{3}{4}x-\frac{1}{4}=2x-6+\frac{1}{4}x\)

\(\Rightarrow\frac{3}{4}x-2x-\frac{1}{4}x=-6+\frac{1}{4}\)

\(\Rightarrow-\frac{3}{2}x=-\frac{23}{4}\)

\(\Rightarrow x=\frac{23}{4}:\frac{3}{2}=\frac{23}{6}\)

\(\Rightarrow\frac{8}{9}x-\frac{1}{3}x=\frac{2}{3}+\frac{11}{3}\)

\(\Rightarrow\frac{5}{9}x=\frac{13}{3}\)

\(\Rightarrow x=\frac{13}{3}:\frac{5}{9}=\frac{39}{5}\)

a; -2\(x\) - 3.(\(x-17\)) = 34 - 2.( - \(x\) + 25)

    - 2\(x\) - 3\(x\) + 51 = 34 + 2\(x\) - 50

       2\(x\) + 2\(x\) + 3\(x\) = - 34 + 50 + 51

            7\(x\)            = 67

               \(x\)           =  67 : 7

                \(x\)         =  \(\dfrac{67}{7}\)

Vậy \(x\) = \(\dfrac{67}{7}\) 

b; 17\(x\) + 3.(- 16\(x\) - 37) = 2\(x\) + 43 - 4\(x\)

    17\(x\) - 48\(x\)  - 111 =  2\(x\) - 4\(x\) + 43

    - 31\(x\) - 2\(x\) + 4\(x\) = 111 + 43

        - \(x\) x (31 + 2 - 4) = 154

        - \(x\) x (33 - 4) =  154

         - \(x\) x 29 = 154

         - \(x\)         = 154 : (-29)

           \(x\)        = - \(\dfrac{154}{29}\)

          Vậy \(x=-\dfrac{154}{29}\)