a) 2x-15=17

    2x     = 17+15 = 32

     x      = 32 : 2 =16

b) \(2^x.4=128\)

    \(2^x=128:4=32\)

Mà \(32=2^5\)

Vậy x = 5

c, 2^x x4=128
=>2^xx2²=2⁷
=>x+2=7
=>x =7-2
=>x=5

   

a) \(\left(x-1\right)^3=125\)

\(\Leftrightarrow\left(x-1\right)^3=5^3\)

\(\Leftrightarrow x-1=5\)

\(\Leftrightarrow x=5+1\)

\(\Leftrightarrow x=6\)

Vậy \(x=6\)

b) \(2^{x+2}-2^x=96\)

\(\Leftrightarrow\left(2^2-1\right)\cdot2^x=96\)

\(\Leftrightarrow\left(4-1\right)\cdot2^x=96\)

\(\Leftrightarrow3\cdot2^x=96\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

Vậy \(x=5\)

c) \(\left(2x+1\right)^3=343\)

\(\Leftrightarrow\left(2x+1\right)^3=7^3\)

\(\Leftrightarrow2x+1=7\)

\(\Leftrightarrow2x=7-1\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

d) \(720:\left[41-\left(2x-5\right)\right]=2^3\cdot5\)

\(\Leftrightarrow720:\left[41-\left(2x-5\right)\right]=2^3\cdot5\left(đk:x\ne23\right)\)

\(\Leftrightarrow720:\left(41-2x+5\right)=8\cdot5\)

\(\Leftrightarrow720:\left(46-2x\right)=40\)

\(\Leftrightarrow\dfrac{720}{46-2x}=40\)

\(\Leftrightarrow\dfrac{720}{2\left(23-x\right)}=40\)

\(\Leftrightarrow\dfrac{360}{23-x}=40\)

\(\Leftrightarrow360=40\left(23-x\right)\)

\(\Leftrightarrow9=23-x\)

\(\Leftrightarrow x=23-9\)

\(\Leftrightarrow x=14\left(đk:x\ne23\right)\)

\(\Leftrightarrow x=14\)

Vậy \(x=14\)

e) \(2^x\cdot7=224\)

\(\Leftrightarrow7\cdot2^x=224\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

Vậy \(x=5\)

f) \(\left(3x+5\right)^2=289\)

\(\Leftrightarrow3x+5=\pm17\)

\(\Leftrightarrow\left[{}\begin{matrix}3x+5=17\\3x+5=-17\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{22}{3}\end{matrix}\right.\)

Vậy \(x_1=-\dfrac{22}{3};x_2=4\)

a)\(\left(x-1\right)^3=125\Leftrightarrow\left(x-1\right)^3=5^3\Leftrightarrow x-1=5\Leftrightarrow x=6\)b)\(2^{x+2}-2^x=96\Leftrightarrow2^x.2^2-2^x=96\Leftrightarrow2^x\left(2^2-1\right)=96\Leftrightarrow2^x.3=96\Leftrightarrow2^x=32\Leftrightarrow x=5\)c)\(\left(2x-1\right)^3=343\Leftrightarrow\left(2x-1\right)^3=7^3\Leftrightarrow2x-1=7\Rightarrow2x=8\Rightarrow x=4\)d)\(720:\left[41-\left(2x-5\right)\right]=2^3.5\)

\(720:\left[41-\left(2x-5\right)\right]=40\Leftrightarrow\left[41-\left(2x-5\right)\right]=720:40=18\)

\(\Leftrightarrow41-2x+5=18\Leftrightarrow36-2x=18\Leftrightarrow2x=18\Leftrightarrow x=9\)

e)\(2^x.7=224\Leftrightarrow2^x=224:7=32\Leftrightarrow2^x=2^5\Leftrightarrow x=5\)

f) \(\left(3x+5\right)^2=289\Leftrightarrow\left(3x+5\right)=17^2\Leftrightarrow3x+5=17\Leftrightarrow3x=12\Leftrightarrow x=4\)

Bai 1

7⁵:7³-343:7

=49-49=0

Bai 2

a. 3^x:3²=243

=> 3^x-2=243

=> x-2=5

=> x=7(bạn viết sai đề câu này phải là 243)

b. x=-1;0;1

c. 2^x.64=2⁶

=> 2^x.2⁶=2⁶

=> 2^x=1

=> x=0

a, 7.7^x+1=343

   7^x+1+1=343

    7^x+2=343=7³

=> x+2=3

      x=3-2=1

b,2³.2^x=64

     2^3+x=64=2⁶

  => 3+x=6

        x=6-3=3

c,(3x-15)⁷=0

  =>  (3x-15)=0

    3x-15=0

    3x=0+15

    3x=15

     x=15:3=5

d,  4^(2x-6)=1

  => 4^(2x-6)=4⁰=1

=>    2x-6=0

        2x=0+6=6

         x=6:2=3

e, (3-x)^10x:(3-x)²⁰=1

Nx:   Một số chia cho chính nó luôn bằng1

Có:   3-x=3-x

=>  10x=20

       x=20:10=2

f, (x-6)³=(x-6)²

Ta có:       Th1:      0³=0²=0

                  =>  (x-6)³=(x-6)²=0

                   =>  x-6 =0

                        x=0+6=6

             Th2:    1³=1²=1

                    =>    (x-6)³=(x-6)²=1

                      =>   x-6=1

                              x=1+6=7

a)(x+810)/7-40=32*5/2

(x+810)/7-40=80

(x+810)/7=80+20

(x+810)/7=120

x+810=120*7

x+810=840

x=840-810

x=30

b)2^x-15=17

2^x=17+15=32=2⁵

=>x=5

c)3^x-25=56

3^x=56+25=81=3⁴

=>x=4

d)x¹⁰=1^x

x=1;0

g)x¹⁰=x

x¹⁰-x=0

x(x⁹-1)=0

=>x=0       hoặc                x⁹-1=0

                                        x⁹=0+1=1=1⁹

Vậy x=1 hoặc x=-1