Ta có: 5².7³.11².x - 5².7².11⁴ = 0

=> 5².7².11²(7x - 11²) = 0

=> 7x - 121 = 0

=> 7x = 121

=> x = 121 : 7

=> x = 121/7

ta có \(5^2.7^3.11^2.x+5^3.7^2.11=0< =>5^2.7^2.11\left(77x+1\right)=0\)

<=> \(77x+1=0< =>x=-\frac{1}{77}\)

\(5^2.7^3.11^2.x+5^3.7^2.11=0\)

=>\(5^2.7^2.11.\left(77x+5\right)=0\)

=>\(77x+5=0\)

=>77x=-5

=>\(x=-\dfrac{5}{77}\)

\(5^2.7^3.11^2.x+5^3.7^2.11=0\)

\(5^2.7^2.11.\left(77x+5\right)=0\)

\(77x+5=0\)

\(77x=-5\)

\(x=\dfrac{-5}{77}\)

\(5^2.7^3.11^2.x+5^3.7^2.11=0\)

\(\Leftrightarrow5^2.7^2.11\left(7.11.x+5\right)=0\)

\(\Leftrightarrow77x+5=0\)

\(\Leftrightarrow77x=-5\)

\(\Leftrightarrow x=-\frac{5}{77}\)

( 3x - 2⁴ ) . 7⁵ = 2.7⁶ .1/2017⁰

( 3x - 2⁴ ) . 7⁵ =235298

( 3x - 2⁴ ) = 235298 : 7⁵ 

( 3x - 2⁴ ) =14

3x = 14 + 2⁴ 

3x = 30

x = 0

dung 100%

\(\left(3x-2^4\right).7^5=2.7^6.\frac{1}{2017^0}\)

\(\Leftrightarrow\left(3x-16\right).7^5=2.7^6.1\)

\(\Leftrightarrow3x-16=\frac{2.7^6}{7^5}\)

\(\Leftrightarrow3x-16=2.7\)

\(\Leftrightarrow3x-16=14\)

\(\Leftrightarrow3x=30\)

\(\Leftrightarrow x=10\)

Nhưng mình làm cách này có được không :  (Tự nhiên nghĩ được)

(3x-2^4).7^5=2.7^6.1/2017^0 

(3x-2^4).7^5=2.7.7^5.1

3x-16=2.7   ( Bớt cả hai vế cho 7^5)

3x=14+16

x=30:3

x=10

1. Tìm x, biết:

a) \(\frac{4}{x}=\frac{8}{6}\). Ta có: \(\frac{8}{6}=\frac{8:2}{6:2}=\frac{4}{3}\Rightarrow x=3\)

b) \(\frac{3}{x-5}=\frac{4}{x+2}\). Ta có: \(5-2=3\)

\(\Rightarrow x=\left(3.5\right)+\left(4.2\right)+3=15+8+3=26\)

c) \(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x=\left(-8\right):\left(-2\right)=4\)

2. Rút gọn

a) \(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}\Leftrightarrow\frac{2^3.2^1.5^2.11.11.7}{2^3.5^2.5^1.7.7.11}\Leftrightarrow\frac{2^1.11}{5^1.7}=\frac{22}{35}\)

b) Tương tự

c) Tương tự

\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{4.6}{8}=3\)

\(\frac{3}{x-5}=\frac{-4}{x+2}\Rightarrow3\left(x+2\right)=-4\left(x-5\right)\)

                                \(\Rightarrow3x+6=-4x+20\)

                                \(\Rightarrow3x+4x=20-6\)

                                \(\Rightarrow7x=14\)

                                \(\Rightarrow x=2\)

\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x^2=\left(-8\right)\left(-2\right)=16\Rightarrow x=\pm4\)

\(\frac{4}{x}=\frac{8}{6}\)

\(\Rightarrow4\cdot6=x\cdot8\)

\(\Rightarrow x=\frac{4\cdot6}{8}\)

\(\Rightarrow x=3\)

b/100x+(1+2+3+...+100)=205550

100x+5050=205550

100x=205550-5050

100x=200500

x=200500/100

x=2005

d/(3x-2⁴).7⁵=2.7⁶.1/2009⁰

(3x-2⁴).7⁵=2.7⁶.1

(3x-2⁴)=2.7⁶:7⁵

(3x-2⁴)=2.7

3x-16=14

3x=14+16

3x=30

x=30/10=3

b) ( \(x\)+ 1 ) + ( \(x\)+ 2 ) + ( \(x\)+ 3 ) + ... + ( \(x\)+ 100 ) = 205550

\(x\)x 100 + ( 1 + 2 + 3 + ... + 100 ) = 205550

\(x\)x 100 + 5050 = 205550

 \(x\)x 100 = 205550 - 5050 

\(x\)x 100 = 200500

\(x\)= 200500 : 100

\(x\)= 2005