mình không hiểu

c) \(3^2+2^4-\left(6^8:6^6-6^2\right)< 5^x< 125\)

\(=9+16-\left(6^{8-6}-36\right)< 5^x< 5^3\)

\(=25-\left(6^2-36\right)< 5^x< 5^3\)

\(=25-\left(36-36\right)< 5^x< 5^3\)

\(=25-0< 5^x< 5^3\)

\(=25< 5^x< 5^3\)

\(=5^2< 5^x< 5^3\)

Vì \(5^2=25\) và \(5^3=125\) nên \(x\) không thể thỏa mãn đề bài

⇒ \(x\) không thỏa mãn đề bài

3.5^x + 4.5^x+1 + 2.5^x+2 = 1825

5^x.(3+4.5+2.5²) = 1825

=> 5^x.73 = 1825

=> 5^x = 25 = 5²

=> x = 2

1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)

`@` `\text {Ans}`

`\downarrow`

`3^3 * x^2 - 2^4 * x^2 = 8^2 * 5 - 4^2 * 3^2`

`=> x^2 . (3^3 - 2^4) = 2^6 . 5 - 2^4 . 3^2`

`=> x^2 . 11 = 2^4 . (2^2 . 5 - 3^2)`

`=> x^2 . 11 = 2^4 . 11`

`=> x^2 . 11 - 2^4 . 11 = 0`

`=> 11 . (x^2 - 16) = 0`

`=> x^2 - 16 = 0`

`=> x^2 = 16`

`=> x^2 = (+-4)^2`

`=> x = `\(\pm4\)

Vậy, `x \in`\(\left\{4;-4\right\}\)

_____

\(\left[\left(\dfrac{1}{2}\right)^2-\left(\dfrac{1}{3}\right)^3\right]x+3^2\cdot2^2=4^2\cdot3\)

`=>`\(\left(\dfrac{1}{4}-\dfrac{1}{27}\right)x+\left(3\cdot2\right)^2=48\)

`=>`\(\dfrac{23}{108}\cdot x+6^2=48\)

`=>`\(\dfrac{23}{108}x=48-6^2\)

`=>`\(\dfrac{23}{108}x=48-36\)

`=>`\(\dfrac{23}{108}x=12\)

`=>`\(x=\dfrac{1296}{23}\)

Vậy, `x = `\(\dfrac{1296}{23}\)

\(3^3.x^2-2^4.x^2=8^2.5-4^3.3^2\)

\(\Leftrightarrow x^2\left(27-16\right)=2^6.5-2^6.9\)

\(\Leftrightarrow11x^2=2^6.\left(5-9\right)=-4.2^6=-2^8\)

\(\Leftrightarrow x^2=-\dfrac{2^6}{11}< 0\)

\(\Rightarrow x\in\varnothing\)

\(\left[\left(\dfrac{1}{2}\right)^2-\left(\dfrac{1}{3}\right)^3\right]x+3^2.2^2=4^2.3\)

\(\Leftrightarrow\left(\dfrac{1}{4}-\dfrac{1}{27}\right)x+36=48\)

\(\Leftrightarrow\dfrac{23}{108}x=12\Leftrightarrow x=\dfrac{12.108}{23}=\dfrac{1296}{23}\)

kết bạn kiểu gì

a)1+3+5+7+9+...+x=1600

=>[(x-1):2+1].(x+1)/2=1600

=>(1/2.x-1/2+1).(x+1)=1600:1/2

=>(1/2.x-1/2+1).(x+1)=3200

=>(x+1)².1/2=3200

=>(x+1)²       =3200:1/2

=>(x+1)²=6400

=>x+1=80

=>x=80-1=79

a ) 1 + 3 + 5 + ... + x = 1600

Theo bài ra ta có :

[ ( x -1 ) : 2 + 1 ]² = 1600

  ( x - 1 ) : 2 + 1    = 40 ( căn bậc 2 của 1600 )

  ( x - 1 ) : 2          = 40 - 1

  ( x - 1 ) : 2          = 39

     x - 1                = 39 . 2

     x - 1                = 78

          x                = 78 + 1

          x                = 79

Vậy x = 79

b ) A = 1.2 + 2.3 + 4.3 + ..... + 99.100

A x 3 = 1.2.3 + 2.3.3 + 4.3.3 + ..... + 99.100.3

A x 3 = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 4.3.(  5 - 2 ) + ... + 99.100.( 101 - 98 )

A x 3 = 1.2.3 - 1.2.0 + 2.3.4 - 1.2.3 + 4.3.5 - 4.3.2 + ..... + 99.100.101 - 99.100.98

A x 3 = 99.100.101

A       = 99.100.101 : 3

A       = 333300

Vậy A = 333300

c ) 

     B = 1.3 + 2.4 + 3.5 + ..... + 99.101

B x 3 = 1.2.3 + 2.4.2 + 5.3.2 + ..... + 99.101.2

B x 3 = 1.3.( 2 - 0 ) + 2.4.( 3 - 1 ) + 5.3.( 4 - 2 ) + ... + 99.101.( 102 - 100 )

B x 3 = 1.2.3 - 1.3.0 + 2.3.4 - 1.2.3 + 4.3.5 - 5.3.2 + ..... + 99.101.102 - 99.101.100

B x 3 = 99.101.102

B       = 99.101.102 : 3

B       = 339966

Vậy B = 339966

d ) C=1.4+2.5+3.6+...+99.102

    C = 1.(2+2) + 2.(3+2) + 3.(4+2)+...+99.(100+2) 

    C = 1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2 

    C = (1.2+2.3+3.4+...+99.100)+2(1+2+3+...+99) 

    C = 333300 + 9900 

    C = 343200

Vậy C = 343200

e ) D = 1.2.3 + 2.3.4 + 3.4.5 + .... + 98.99.100

=> 4D = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 98.99.100.4

=> 4D = 1.2.3.4 + 2.3.4.( 5 - 1 ) + 3.4.5.( 6 - 2 ) + .... + 98.99.100.( 101 - 97 )

=> 4D = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + .... + 98.99.100.101 - 97.98.99.100

=> 4D = ( 1.2.3.4 - 1.2.3.4 ) + ( 2.3.4.5 - 2.3.4.5 ) + ...... + ( 97.98.99.100 - 97.98.99.100 ) + 98.99.100.101

=> 4D = 98.99.100.101

=> S = 98.99.100.10 : 14 

=> S = 24497550

Ta có:

\(\frac{2^3.3^4}{2^2.3^2.5}=\frac{2.3^2}{5}=\frac{18}{5}\)

\(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}=\frac{2.11}{5.7}=\frac{22}{35}\)

Lời giải:

1.

$3^{x+2}+4.3^{x+1}=7.3^6$

$3^{x+1}.3+4.3^{x+1}=7.3^6$

$3^{x+1}(3+4)=7.3^6$

$3^{x+1}.7=7.3^6$

$\Rightarrow 3^{x+1}=3^6$

$\Rightarrow x+1=6$

$\Rightarrow x=5$

2.

$5^{x+4}-3.5^{x+3}=2.5^{11}$

$5^{x+3}.5-3.5^{x+3}=2.5^{11}$

$5^{x+3}(5-3)=2.5^{11}$

$2.5^{x+3}=2.5^{11}$

$\Rightarrow 5^{x+3}=5^{11}$

$\Rightarrow x+3=11$

$\Rightarrow x=8$

3.

$4^{x+3}-3.4^{x+1}=13.4^{11}$

$4^{x+1}.4^2-3.4^{x+1}=13.4^{11}$

$4^{x+1}.16-3.4^{x+1}=13.4^{11}$

$13.4^{x+1}=13.4^{11}$

$\Rightarrow 4^{x+1}=4^{11}$

$\Rightarrow x+1=11$
$\Rightarrow x=10$

Ta có:\(5^{x+4}-3\cdot5^{x+3}=2\cdot5\)

\(5^x\cdot5^4-3\cdot5^x\cdot5^3=10\)

\(5^x\left(5^4-3\cdot5^3\right)=10\)

\(5^x\cdot250=10\)

\(5^x=10:250\)

\(5^x=\frac{1}{25}\)

\(5^x=5^{-2}\)

\(\Rightarrow x=-2\)

\(5^{x+4}-3.5^{x+3}=2.5\)

\(\Rightarrow5^{x+3}.5-3.5^{x+3}=2.5\)

\(\Rightarrow5^{x+3}.\left(5-3\right)=2.5\)

\(\Rightarrow5^{x+3}.2=2.5\)

\(\Rightarrow5^{x+3}=5\)

\(\Rightarrow x+3=1\)

\(\Rightarrow x=-2\)

Vậy \(x=-2\)