Tìm \(x\) câu a:

\(\frac13.x\) + \(\frac25.\left(x+1\right)\) = 0

\(\frac{5}{15}x\) + \(\frac{6}{15}x\) + \(\frac25\) = 0

\(\frac{11}{15}x\) = - \(\frac25\)

\(x=-\frac25:\frac{11}{15}\)

\(x\) = - \(\frac25\times\frac{15}{11}\)

\(x\) = - \(\frac{6}{11}\)

Vậy \(x=-\frac{6}{11}\)

Tìm \(x\) câu b:

\(x\) x 25% = 0,5

\(x\times0,25\) = 0,5

\(x=0,5:0,25\)

\(x=2\)

Vậy \(x=2\)

Câu 1a:

1/3x + 2/5(x + 1) = 0

1/3x + 2/5x + 2/5 = 0

1/3x + 2/5x = - 2/5

x(1/3 + 2/5) = -2/5

x.(5/15 + 6/15) = -2/5

x.11/15 = - 2/5

x = - 2/5 : 11/15

x = - 6/11

Vậy x = -6/11

Câu b:

x . 25%. x = 0,5

x.x = 0,5 : 25%

x^2 = 2

x = - \(\sqrt2\); x = \(\sqrt2\)

Vậy x ∈ {- \(\sqrt2\); \(\sqrt2\) )

Câu 1a:

1/3x + 2/5(x + 1) = 0

1/3x + 2/5x + 2/5 = 0

1/3x + 2/5x = - 2/5

x(1/3 + 2/5) = -2/5

x.(5/15 + 6/15) = -2/5

x.11/15 = - 2/5

x = - 2/5 : 11/15

x = - 6/11

Vậy x = -6/11

Câu b:

x . 25%. x = 0,5

x.x = 0,5 : 25%

x^2 = 2

x = - \(\sqrt2\); x = \(\sqrt2\)

Vậy x ∈ {- \(\sqrt2\); \(\sqrt2\) )

\(A\frac{27^4.8^{17}}{9^6.32^3}=\frac{\left(3^3\right)^4.\left(2^3\right)^{17}}{\left(3^2\right)^6.\left(2^5\right)^3}=\frac{3^{12}.2^{51}}{3^{12}.2^{15}}=\frac{3^{12}.2^{15}.2^{36}}{3^{12}.2^{15}}=2^{36}\) 

\(B=\frac{72^3.54^3:8^3}{108^5:4^5}=\frac{\left(72.54:8\right)^3}{\left(108:4\right)^5}=\frac{486^3}{27^5}=\frac{\left(3^5.2\right)^3}{\left(3^3\right)^5}=\frac{3^{15}.2^3}{3^{15}}=2^3=8\) 

Bài 2 

A = 2 +2² + 2³ + 2⁴ + ....+ 2¹⁰⁰ 

A = ( 2+2² ) + (2³ + 2⁴ ) + ....+ (2⁹⁹ + 2¹⁰⁰ )

A = 2(1+2 ) + 2³ (1+2 ) + ...+ 2⁹⁹(1+2) 

A = 2.3 + 2³.3 + ....+ 2⁹⁹ .3 

A = 3(2+2³ + ...+ 2⁹⁹ )  

=> A \(⋮\) 3 ( đpcm ) 

Bài 3 

a, 2.3^x = 3¹² .34 + 20 .27⁴ 

2.3^x = 3¹²  . 34 + 20 . (3³ ) ⁴ 

2.3^x = 3¹² .34 + 20 .3¹²

2.3^x = 3¹²(34+20 ) 

2.3^x = 3¹² . 54 

2.3^x = 3¹² . 27 .2 

2.3^x = 3¹² . 3³ .2 

2.3^x = 3¹⁵ .2 

=> x=15 

b , (2^x +1 ) ² + 3.(2² + 1 ) = 2² .10 

 (2^x +1 ) ²  + 3.(4+1 ) = 4.10 

 (2^x +1 ) ²  + 3.5 = 40 

(2^x +1 ) ²  + 15 = 40 

(2^x +1 ) ²  = 40-15

(2^x +1 ) ²  = 25 

(2^x +1 ) ²   = 5² 

=> 2^x + 1 = 5 

2^x  = 5-1 

2^x = 4 

2^x = 2² 

=> x=2 

a,Ư(25)={1;5;25}

\(\Rightarrow\)2x+1\(\in\left\{1;5;25\right\}\)

\(\Rightarrow x\in\left\{0;2;12\right\}\)

bTa có : \(x\inƯC\left(60;150;210\right)\)

Ư(60)={1;2;3;4;5;6;10;12;15;20;30;60}

Ư(150)={1;2;3;5;6;10;15;25;30;50;125;150}

Ư(210)={1;2;3;5;6;7;10;15;30;35;42;70;105;210}

\(\Rightarrow x\in\left\{1;2;3;5;6;10;15;30\right\}\)

mà x>25 nên x=30

kcj

a) \(\left(19x+2\times5^2\right):14=\left(13-8\right)^2-4^2\)

\(\Rightarrow\left(19x+50\right):14=5^2-4^2=25-16=9\)

\(\Rightarrow19x+50=126\)

\(\Rightarrow19x=76\Rightarrow x=4\)

Vậy x = 4

b) \(2\times3^2=10\times3^{12}+8\times27^4\)

\(\Rightarrow2\times3^2=10\times\left(3^3\right)^4+8\times27^4\)

\(\Rightarrow2\times3^2=27^4\times\left(10+8\right)\)

\(\Rightarrow18=27^4\times18\)

\(\Rightarrow27^4\times18-18=0\Rightarrow18\times\left(27^4-1\right)=0\)

=> Không thấy biến x đâu cả

c) Ta thấy 3³ = 27

\(\Rightarrow3^{2x-5}=3^3\Rightarrow2x-5=3\Rightarrow2x=8\Rightarrow x=4\)

Vậy x = 4

d) \(3^{x+1}-x=80\Rightarrow3^{x+1}=81\)

Ta thấy 3⁴ = 81

\(\Rightarrow3^{x+1}=3^4\Rightarrow x+1=4\Rightarrow x=3\)

Vậy x = 3

a) \(2^{4x+1}-8^{x+2}=0\)\(\Leftrightarrow2^{4x+1}-2^{3\left(x+2\right)}=0\)

\(\Leftrightarrow2^{4x+1}-2^{3x+6}=0\)\(\Leftrightarrow2^{4x+1}=2^{3x+6}\)

\(\Leftrightarrow4x+1=3x+6\)\(\Leftrightarrow4x-3x=6-1\)\(\Leftrightarrow x=5\)

Vậy \(x=5\)

b) \(3^2.9^{2x}=27^{x+3}\)\(\Leftrightarrow3^2.3^{2.2x}=3^{3\left(x+3\right)}\)\(\Leftrightarrow3^2.3^{4x}=3^{3x+9}\)

\(\Leftrightarrow3^{2+4x}=3^{3x+9}\)\(\Leftrightarrow2+4x=3x+9\)\(\Leftrightarrow4x-3x=9-2\)\(\Leftrightarrow x=7\)

Vậy \(x=7\)

c) \(8^{2x}.64^2=16^{x+4}\)\(\Leftrightarrow2^{3.2x}.2^{6.2}=2^{4\left(x+4\right)}\)\(\Leftrightarrow2^{6x}.2^{12}=2^{4\left(x+4\right)}\)

\(\Leftrightarrow2^{6x+12}=2^{4x+16}\)\(\Leftrightarrow6x+12=4x+16\)\(\Leftrightarrow6x-4x=16-12\)

\(\Leftrightarrow2x=4\)\(\Leftrightarrow x=2\)

Vậy \(x=2\)