Ta có: \(\left(\frac{1}{81}\right)^x.27^{2x}=\left(-9\right)^4\)

Áp dụng công thức: \(a^x.b^x=\left(a.b\right)^x\)    

Ta lại có: \(\left(\frac{1}{81}.27^2\right)^x=9^4\)

         \(\Leftrightarrow9^x=9^4\)

         \(\Leftrightarrow x=4\)

Vậy \(x\in\left\{4\right\}\)

\(\left(\frac{1}{81}\right)^x.27^{2x}=\left(-9\right)^4\)

\(\Rightarrow\) \(\left(\frac{1}{3}\right)^{4x}.3^{6x}=3^8\)

\(\Rightarrow\) \(\frac{3^{6x}}{3^{4x}}=3^8\)

\(\Rightarrow\) \(3^{2x}=3^8\)

\(\Rightarrow\) \(2x=8\)

\(\Rightarrow\) x = 4

\(\frac{1}{2}^{3x-1}=\frac{1}{32}\)

\(\Leftrightarrow\frac{1}{2}^{3x-1}=\frac{1}{2}^5\)

\(\Leftrightarrow3x-1=5\)

\(\Leftrightarrow3x=6\)

\(\Leftrightarrow x=2\)

Tìm x

\(\left(\frac{1}{2}\right)^{3x-1}=\frac{1}{32}\)

\(\left(\frac{1}{2}\right)^{3x-1}=\left(\frac{1}{2}\right)^5\)

\(\Rightarrow3x-1=5\)

\(\Rightarrow3x=6\)

\(\Rightarrow x=2\)

Vậy \(x=2\).

Ta có: \(2.3^x-405=3^{x-1}\)

    \(\Leftrightarrow2.3^x-3^x:3^1=405\)

    \(\Leftrightarrow3^x.\left(2-\frac{1}{3}\right)=405\)

    \(\Leftrightarrow3^x.\frac{5}{3}=405\)

    \(\Leftrightarrow3^x=81.3\)

    \(\Leftrightarrow3^x=3^4.3\)

    \(\Leftrightarrow3^x=3^5\)

    \(\Leftrightarrow x=5\)

Vậy \(x\in\left\{5\right\}\)

mình ko bt làm

\(\left(\frac{3}{4}-x\right)^3=\frac{1}{64}\)

\(\Leftrightarrow\left(\frac{3}{4}-x\right)^3=\frac{1}{4}^3\)

\(\Leftrightarrow\frac{3}{4}-x=\frac{1}{4}\)

\(\Leftrightarrow x=\frac{1}{2}\)

Trả lời :

\(\left(x-\frac{1}{2}\right)\left(1+5x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=0\\1+5x=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\5x=-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{5}\end{cases}}\)

\(\left(x-\frac{1}{2}\right)\left(1+5x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}=0\\1+5x=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\5x=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{5}\end{cases}}\)

\(\frac{x+2}{5}=\frac{2-3x}{3}\)

\(\Leftrightarrow3\left(x+2\right)=5\left(2-3x\right)\)

\(\Leftrightarrow3x+6=10-15x\)

\(\Leftrightarrow3x+15x=10-6\)

\(\Leftrightarrow18x=4\)

\(\Leftrightarrow x=\frac{2}{9}\)

\(\frac{x+2}{5}=\frac{2-3x}{3}\)

\(\Leftrightarrow3\left(x+2\right)=5\left(2-3x\right)\)

\(\Leftrightarrow3x+6=10-15x\)

\(\Leftrightarrow3x+15x=10-6\)

\(\Leftrightarrow18x=4\)

\(\Leftrightarrow x=\frac{4}{18}=\frac{2}{9}\)

\(\frac{1}{3}x-\frac{2}{5}\left(x+1\right)=0\)

\(\Rightarrow\frac{1}{3}x-\frac{2}{5}x-\frac{2}{5}=0\)

\(\Rightarrow-\frac{1}{15}x=\frac{2}{5}\)

\(\Rightarrow x=-6\)

3/4+1/4x=1/2+1/2x

1/2x+1/4x=1/2+3/4

1/2x+1/4x=5/4

x×(1/2+1/4)=5/4

x×3/4=5/4

x=5/4:3/4

x=5/4×4/3

x=5/3

vậy x=5/3

\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có :

\(\frac{x^2}{9}=\frac{y^2}{16}=\frac{x^2+y^2}{9+16}=\frac{100}{25}=4\)

Suy ra :

+) \(\frac{x}{3}=4\Rightarrow x=12\)

+) \(\frac{y}{4}=4\Rightarrow y=16\)

cái b là = 34 nha mn

A=1²+2²+3²+...+20²

A= 1.1 + 2.2 + 3.3 +....+20.20

A= 1(2-1) + 2(3-1) + 3(4-1)+....+20(21-1)

A= 1.2 - 1.1 + 2.3 -2.1 + 3.4- 1.3 +...+ 20.21-1.20

A= 1.2 + 2.3 +3.4+.....+ 20.21 - (1 +2 + 3 +...+20)

Đặt B= 1.2 + 2.3 + 3.4 +...+20.21

3B = 1.2.3 + 2.3.3 + 3.4.3 +...+20.21.3

3B= 1.2.3 + 2.3 (4-1) + 3.4(5-1)+...+20.21(22-19)

3B= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 1.3.4 +....+20.21.22- 19.20.21

3B= 20.21.22

3B= 9240

B= 9240:3

B= 3080

Ta có: A= 3080 -(1 +2 + 3 +...+20)

A= 2870

Vậy....

A = 1² + 2² + 3² + ... + 20²

= 1.1 + 2.2 + 3.3 + ... + 20.20

= 1.(2 - 1) + 2.(3 - 1) + 3.(4 - 1) + ... + 20.(21 - 1)

= 1.2 + 2.3 + 3.4 + ... + 20.21 - (1 + 2 + 3 + ... + 20)

= 1.2 + 2.3 + 3.4 + ... + 20.21 - 210

Đặt B = 1.2 + 2.3 + 3.4 + ... + 20.21

=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 20.21.3

=> 3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 20.21.(22 - 19)

=> 3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 20.21.22 - 19.20.21

=> 3B = 20.21.22

=> 3B = 9240

=> B = 3080

Thay B vào A ta có

A = 3080 - 210 = 2870

Vậy A = 2870