\(5^{2x+1}\cdot5^{2x+2}-5^x\cdot5^{3x+2}=100\)

\(\Leftrightarrow5^{4x+3}-5^{4x+2}=100\)

\(\Leftrightarrow625^x\left(5^3-5^2\right)=100\)

\(\Leftrightarrow625^x=1\)

hay x=0

\(\Rightarrow5^{2x+1+2x+2}-5^{x+3x+2}=100\\ \Rightarrow5^{4x+3}-5^{4x+2}=100\\ \Rightarrow5^{4x+2}\left(5-1\right)=100\\ \Rightarrow5^{4x+2}=25=5^2\\ \Rightarrow4x+2=2\Rightarrow x=0\)

\(5^{2x+1}.5^{2x+2}-5^x.5^{3x+2}=100\)

\(5^{4x+3}-5^{4x+2}=100\)

\(5^{4x+2}\left(5-1\right)=100\)

\(5^{4x+2}=25\)

4x+2=2

4x=0

x=0

1.

a) \(5x.5x.5x=\left(5x\right)^3.\)

b) \(x^1.x^2.....x^{2006}=x^{\frac{\left(2006+1\right).2006}{2}=}x^{2013021}.\)

c) \(x^1.x^4.x^7.....x^{100}=x^{\frac{\left(100+1\right).\left(\frac{100-1}{3}+1\right)}{2}}=x^{1717}.\)

d) \(x^2.x^5.x^8.....x^{2003}=x^{\frac{\left(2003+2\right).\left(\frac{2003-2}{3}+1\right)}{2}}=x^{669670}.\)

2.

\(2^x+80=3^y\)

Với \(x>0\Rightarrow2^x\) chẵn

Và 80 chẵn

\(\Rightarrow2^x+80\) chẵn.

Mà \(3^y\) lẻ

\(\Rightarrow x< 0.\)

Mà \(x\in N\)

\(\Rightarrow x=0.\)

\(\Rightarrow2^0+80=3^y\)

\(\Rightarrow1+80=3^y\)

\(\Rightarrow3^y=81\)

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

\(\Rightarrow y=4.\)

Vậy \(\left(x;y\right)=\left(0;4\right).\)

Chúc bạn học tốt!

1.viết tích dưới dạng lũy thừa

a.5x.5x.5x

=(5x)\(^3\)

b.x\(^1\) . x \(^2\).......x \(^{2006}\)

=x \(^{2013021}\)

c.x\(^1\).x \(^4\) .x \(^7\)......x \(^{100}\)

=x \(^{1717}\)

d.x \(^2\) .x \(^5\).x \(^8\).......x\(^{2003}\)

=x \(^{669670}\)

2 \(^x\)+80=3\(^y\)

ta có 3\(^y\)lẻ nên 2 \(^x\)+80 lẻ .

Với x \(\ge\)1

thì 2 \(^x\)+80 chẵn không thỏa mãn

nên x=0

=>1+80=3\(^y\)

=>81=3\(^y\)

=>3\(^4\)=3\(^y\)

=>y=4

ai làm giúp mik đi

ko đó thì sao

Bài 1 :

a) 3. ( 5x - 7 )2 = 507

3 . 5x = 507 -72

3.5x = 435

x = 435 : 3.5

x = 29

d) 52x + 3 - 22 = 112

52x + 3 = 112 + 22

52x + 3 = 134

x = 134 - 52 + 3

x = 79

c) 3.(5x - 7).2 = 507

    3.2.(5x - 7) = 507

       6.(5x - 7) = 507

           5x - 7  = 507 : 6

           5x - 7  =\(\frac{169}{2}\)

                 5x = \(\frac{169}{2}\)+ 7

                 5x = \(\frac{183}{2}\)

                   x = \(\frac{183}{2}\):5

                   x = \(\frac{183}{10}\)

     Vậy x = \(\frac{183}{10}\)

d) 52x + 3 - 22 = 112

          52x - 19 = 112

                 52x = 112 - 19

                 52x = 93

                     x = 93 : 52

                     x = \(\frac{93}{52}\)

     Vậy x = \(\frac{93}{52}\)

     Nếu bạn thấy sai thì rep mình nha

a)\(\left(5x-1\right)^2-\left(5x-4\right)\left(5x+4\right)=7\)

\(\Leftrightarrow25x^2-10x+1-25x^2+16=7\)

\(\Leftrightarrow-10x=-10\)

\(\Leftrightarrow x=1\)

b) k hiểu đề

a) A= (5x-2).(x+1)-(x-3).(5x+1)-17(x+3)

=> A= 5x²+5x-2x-2-5x²-x+15x+3-17x-51

=> A= -50

b) B= (6x-5) × ( x+8) - (3x-1) × (2x+3) - 9(4x-3)

=> B= 6x²+48x-5x-40-6x²-9x+2x+3-36x+27

=> B= -10

c) C = x(x³ + x² - 3x -2 ) - ( x² -2 ) × ( x²+x -1 )

=> C= x⁴+x³-3x²-2x-x⁴+x³+3x²-2x-2

=> C= 2x³-4x-2

= x ^1 +100 =  x^101

\(x\times x^2\times x^3\times x^4\times...\times x^{100}=x^{1+2+3+4+...+100}=x^{101\times500}=x^{5050}\)

\(x\times x^2\times x^3\times x^4\times...\times x^{100}\)

\(=x^{\left(1+100\right)\times100\div2}\)

\(=x^{5050}\)

nha

Áp dụng công thức: Nhân 2 lũy thừa cùng cơ số.
Ta có:
\(x\times x^2\times x^3\times...\times x^{100}\)
\(=x^{1+2+3+...+100}\)
\(x=5050\)

\(x.x^2.x^3...x^{100}=x^{1+2+3+...+100}\)

Đặt \(3^{1+2+3+...+100}=3^A\)

Ta có:

\(A=1+2+3+...+100\)

\(\Rightarrow A=100+99+98+...+1\)

\(\Rightarrow A=\left(1+100\right)+\left(2+99\right)+\left(3+98\right)+...+\left(100+1\right)\) ( 50 cặp số )

\(\Rightarrow A=101+101+101+...+101\)  ( 50 số 101 )

\(\Rightarrow A=101.50\)

\(\Rightarrow A=5050\)

\(\Rightarrow3^A=3^{5050}\)

Vậy \(x.x^2.x^3...x^{100}=x^{5050}\)

Dấu chấm thay cho dấu nhân nhé!