đặt 5 ra ngoài rồi làm như bình thường

5(1/2.3+1/3.4+...+1/x(x+1)=64/13

5.(1/2-1/3+1/3-1/4+...+1/x-1/x+1)=64/13

5(1/2-1/x+10)=64/13

bạn tự làm tiếp nha mình bận rồi

\(\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{x\left(x+1\right)}=\frac{64}{13}\)

\(\Leftrightarrow5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{64}{13}\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{64}{13}\div5\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{64}{65}\)

\(\Leftrightarrow\frac{1}{x+1}=1-\frac{64}{65}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{65}\)

\(\Rightarrow x+1=65\Rightarrow x=65-1=64\)

\(\text{Vậy }x=64\)

Bài 1:

29.(85-47)+85.(47-29)

=29.38+85.18

=1102+1530

 =2632

BÀI 2

a, 15x = -75

        x =( -75) : 15

        x = -5

Vậy x= -5                                                            

b,-5x+8=-27

     -5x    = -27 - 8 

       -5x= -35

          x =-35 : -5

           x = 7

Vậy x = 7

c,3.(17 + x ) = - 42

       17 + x     = - 42 : 3

         17 + x    = -14

                x      = - 14 - 17

                 x = -31

Vậy x = - 31

d,-10 -( 2x -16) = 0

           2x - 16 = 10-0

           2x - 16 = 10

            2x = 10 +16

             2x = 26

                 x = 26 : 2

                  x = 13

 Vậy x = 13

e,( mik ko bít làm)

f,( tự làm nghen bạn)

a, 3^x=162:2

3^x=81

Vì 81=3x3x3x3

=> x=4

b, 2^x-15=17

2^x=17+15

2^x=32

32=2x2x2x2x2

=> x=5

c, x^2=100 Mà 100=10x10

=> x=10

d, x^3=64

Vì 64=4x4x4

=> x=4

a)2.3^2x-1=64

3^2x-1=64:2

3^2x-1=32

2x-1=32/3

2x=35/3

x=35/6

b)

câu 1 dễ

a. 2.3^x = 10 . 3¹² + 8 . 27⁴

 2.3^x = 10 . 3¹² + 8 . ( 3³ )⁴

 2.3^x = 10 . 3¹² + 8 . 3¹²

 2.3^x = 3¹² . ( 10 + 8 ) = 3¹² . 18

3^x = 3¹² . 9

3^x = 3¹² . 3²

3^x = 3¹⁴ => x = 14

b. 64 . 4^x = 4⁵

4³ . 4^x = 4⁵

4^3+x = 4⁵

3 + x =5

x = 5 - 3 = 2

c. 2^x = 4 . 128

2^x = 2² . 2⁷

2^x = 2⁹ => x = 9

d. Mik 0 bik làm do đề khó hiểu quá nhé!!! :))

e. ( x⁵ )¹⁰ = x

x⁵⁰ = x

x⁵⁰ - x = 0 => x . x⁴⁹ - x = 0

x . ( x⁴⁹ - 1 ) = 0

=> x = 0 hoặc  x⁴⁹ - 1 = 0

=> x = 0 hoặc  x⁴⁹ = 1 = 1⁴⁹

=> x = 0 hoặc x = 1

\(a,\left(7x-11\right)^3=2^5.5^2+200.\)

\(\left(7x+11\right)^3=32.25+200.\)

\(\left(7x+11\right)^3=800+200.\)

\(\left(7x-11\right)^3=1000.\)

\(\left(7x-11\right)^3=10^3.\)

\(\Rightarrow7x-11=10.\)

\(\Rightarrow x=\left(10+11\right):3=7\in Z.\)

Vậy.....

\(b,3^x+25=26.2^2+2.3^0.\)

\(3^x+25=26.4+2.\)

\(3^x+25=104+2.\)

\(3^x+25=106.\)

\(3^x=106-25.\)

\(3^x=81.\)

\(3^x=3^4\Rightarrow x=4\in Z.\)

Vậy.....

\(c,2^x+3.2=64.\)(có vấn đề).

\(d,5^{x+1}+5^x=750.\)

\(5^x.5^1+5^x+1=750.\)

\(5^x\left(5^1+1\right)=750.\)

\(5^x\left(5+1\right)=750.\)

\(5^x.6=750.\)

\(5^x=750:6.\)

\(5^x=125.\)

\(5^x=5^3\Rightarrow x=3\in Z.\)

Vậy.....

\(e,x^{15}=x.\)

\(\Rightarrow x\left(x^{14}-1\right)=0\Rightarrow\left\{{}\begin{matrix}x=0\\x=1\end{matrix}\right..\)

\(f,\left(x-5\right)^4=\left(x-5\right)^6.\)

\(\Leftrightarrow\left(x-5\right)^4-\left(x-5^6\right)=0.\)

\(\Leftrightarrow\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0.\)

\(\Leftrightarrow\left(x-5\right)^4\left(1-x+5\right)\left(1+x-5\right)=0.\)

\(\Leftrightarrow\left(x-5\right)^4\left(6-x\right)\left(x-4\right)=0.\)

\(\Leftrightarrow\left(x-5\right)^4=0\Rightarrow x-5=0\Rightarrow x=5\in Z.\)

\(6-x=0\Rightarrow x=6\in Z.\)

\(x-4=0\Rightarrow x=4\in Z.\)

Vậy.....