\(\left(-7\right)^x=\frac{1}{49}\)

=>\(\left(-7\right)^x=\frac{1}{\left(-7\right)^2}\)

=>\(\left(-7\right)^x=\left(-7\right)^{-2}\)

=>x=-2

câu thứ 2 sai đề hay sao á

a ) \(\left(-7\right)^x=\frac{1}{49}\)

\(\left(-7\right)^x=\frac{1}{\left(-7\right)^2}\)

\(\left(-7\right)^x=\frac{1}{\left(-7\right)^{-2}}\)

=> \(x=-2\)

b ) \(\left(-2\right)^x=-0,125\)

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

\(\Rightarrow x=-3\)

1. \(x=-2\)
2. \(x=-1\)
3. \(x=-2\)
4. \(x=-2\)
5. \(x=-1\)

chỉ cách giải luôn nha bạn chỉ rõ mới k

a, \(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}=\frac{13}{90}\)

⇒ \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{13}{90}\)

⇒ \(\frac{1}{5}-\frac{1}{x+1}=\frac{13}{90}\)

⇒ \(\frac{1}{x+1}=\frac{1}{5}-\frac{13}{90}\)

⇒ \(\frac{1}{x+1}=\frac{18}{90}-\frac{13}{90}\)

⇒ \(\frac{1}{x+1}=\frac{1}{18}\)

⇒ x + 1 = 18

⇒ x = 17

Vậy x = 17

b, \(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x\left(x+3\right)}=\frac{49}{148}\)

⇒ \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x\left(x+3\right)}=\frac{49.3}{148}\)

⇒ \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{147}{148}\)

⇒ \(1-\frac{1}{x+3}=\frac{147}{148}\)

⇒ \(\frac{1}{x+3}=1-\frac{147}{148}\)

⇒ \(\frac{1}{x+3}=\frac{1}{148}\)

⇒ x + 3 = 148

⇒ x = 145

Vậy x = 145

cách 1:=> (x - 7)^(x+1)= (x-7)^(x+11) 
 

TH1: x-7=0 => x=7 => 0^8=0^18 (TM) 
 

TH2: x-7=1 => x=8 (TM) 
 

TH3: x khác 7 và 8 => x+1=x+11 => vô lý => loại 
 

KL: x = 7 hoặc x=8

( x-7)^( x+1) - ( x-7)^(x+11) = 0 
 

( x-7)^( x+1) - ( x-7)^(x+1)*x^10 = 0 
 

( x-7)^( x+1) (1-x^10) = 0 

tới đây dễ òi

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

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

\(\Rightarrow x-1=-5\)

\(\Rightarrow x=-5+1=-4\)

làm 1 bài mẫu nha

a) \(\left(\frac{1}{3}.x\right):\frac{2}{3}=\frac{25}{6}\)

\(\Rightarrow\frac{1}{3}x=\frac{25}{9}\)

\(\Rightarrow x=\frac{25}{9}:\frac{1}{3}\)

\(\Rightarrow x=\frac{25}{3}\)

các bài sau dễ lắm

a) \(\left(\frac{1}{3}x\right):\frac{2}{3}=1\frac{2}{3}:\frac{2}{5}\)

\(\Rightarrow\frac{1}{3}x:\frac{2}{3}=\frac{25}{6}\)

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

\(\Rightarrow x=\frac{5}{3}:\frac{1}{3}\)

\(\Rightarrow x=5\)

a)

Điều kiện: $x\ne-2,-5,-10,-17.$

$\dfrac3{(x+2)(x+5)}+\dfrac5{(x+5)(x+10)}+\dfrac7{(x+10)(x+17)}=\dfrac{x}{(x+2)(x+17)}$

$\Leftrightarrow\dfrac1{x+2}-\dfrac1{x+5}+\dfrac1{x+5}-\dfrac1{x+10}+\dfrac1{x+10}-\dfrac1{x+17}=\dfrac{x}{(x+2)(x+17)}$

$\Leftrightarrow\dfrac1{x+2}-\dfrac1{x+17}=\dfrac{x}{(x+2)(x+17)}$

$\Leftrightarrow\dfrac{15}{(x+2)(x+17)}=\dfrac{x}{(x+2)(x+17)}$

$\Leftrightarrow x=15.$

b)

Điều kiện: $x\ne1,3,8,20.$

$\dfrac2{(x-1)(x-3)}+\dfrac5{(x-3)(x-8)}+\dfrac{12}{(x-8)(x-20)}-\dfrac1{x-20}=-\dfrac34$

$\Leftrightarrow\left(\dfrac1{x-3}-\dfrac1{x-1}\right)+\left(\dfrac1{x-8}-\dfrac1{x-3}\right)+\left(\dfrac1{x-20}-\dfrac1{x-8}\right)-\dfrac1{x-20}=-\dfrac34$

$\Leftrightarrow-\dfrac1{x-1}=-\dfrac34$

$\Leftrightarrow\dfrac1{x-1}=\dfrac34$

$\Leftrightarrow4=3(x-1)$

$\Leftrightarrow3x=7$

$\Leftrightarrow x=\dfrac73.$