\(7^{x+2}+2.7^{x+1}=345\)

\(7^{x-1}.7^3+2.7^{x-1}=345\)

\(7^{x-1}.\left(7^3+2\right)=345\)

\(7^{x-1}.345=345\)

\(7^{x-1}=1\)

\(7^{x-1}=7^0\)

\(\Rightarrow x-1=0\)

\(x=1\)

\(1,\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{x+y}{2+5}=\dfrac{21}{7}=3\\ \Rightarrow\left\{{}\begin{matrix}x=6\\y=15\end{matrix}\right.\\ 2,7x=3y\Rightarrow\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{x-y}{3-7}=\dfrac{16}{-4}=-4\\ \Rightarrow\left\{{}\begin{matrix}x=-12\\y=-28\end{matrix}\right.\\ 3,\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{7}=\dfrac{x-y-z}{5-6-7}=\dfrac{36}{-8}=-\dfrac{9}{2}\\ \Rightarrow\left\{{}\begin{matrix}x=-\dfrac{45}{2}\\y=-27\\z=-\dfrac{63}{2}\end{matrix}\right.\\ 4,x:y:z=3:5:7\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{2x+3y-z}{6+15-7}=\dfrac{-14}{14}=-1\\ \Rightarrow\left\{{}\begin{matrix}x=-3\\y=-5\\z=-7\end{matrix}\right.\)

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

\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{7}=\dfrac{x-y-z}{5-6-7}=\dfrac{36}{-8}=\dfrac{-9}{2}\)

\(x=\dfrac{-45}{2}\)

\(y=-27\)

\(z=\dfrac{-63}{2}\)

\(7x.\left(x-2\right)-5.\left(x-1\right)=7x^2+3\)

\(7x^2-14x-5x+5=7x^2+3\)

\(7x^2-19x+5=7x^2+3\)

\(7x^2-19x+5-\left(7x^2+3\right)=0\)

\(7x^2-19x+5-7x^2-3=0\)

\(-19x+2=0\)

\(-19x=0-2\)

\(-19x=-2\)

\(x=\frac{2}{19}\)

7^x+2+2.7^x-1=345

=>7^x-1(7³+2)=345

=>7^x-1=345:345=1

=>x-1=0

=>x=1

7^x-1 . 7^x+3 + 2. 7^x-1 = 345

7^x-1 .(7^x+3 + 2)  =345

7^x-1. (7^x+3 + 2) = 7^x+3 -2

7^x-1                    =(7^x+3 - 2) : (7^x+3 +2)

7^x-1                    = 0

=> x-1                  = 1

chắc chắn luôn

a) 72.6² - 72.16 + 72.8 

= 72.36 - 72.16 + 72.8

= 72 . ( 36 - 16 + 8 )

= 72 . 28 = 2016

b) 8.2^x-1 = 256 

16^x-1 = 16² 

x - 1 = 2 

     x = 2 + 1 

     x = 3

c) 3.5^x - 35 = 5.2³

3.5^x - 35 = 40

3.5^x = 40 + 35

3.5^x = 75

5^x = 75 : 3 = 25

5^x = 5²

=> x = 2

d) 345 - ( 7x + 23 ) = 1722 : 6 = 287

7x + 23 = 345 - 287 

7x + 23 = 58

7x = 58 - 23 = 35

7x = 35

  x = 35 : 7

  x = 5

b) 2^x-1 = 256 : 8 

2^x-1 = 32

ta thấy : 32 = 2^5 

cơ số = cơ số 

=> x - 1 = 5 

x = 5 = 1 

x = 6

a) x + ( x+1) + (x+2)+...+(x+9)=345

<=> 10x + (1 + 2 + 3 + ..... + 9) = 345

=> 10x + 45 = 345

=> 10x = 300

=> x = 30

a:1/5 + a:0,25 + a = 2,7x 0,1

=>a:(1/5 + 0.25 + 1) = 0.27

=>a:1.45 = 0.27

=> a = 0.27 x 1.45

a:1\5+a:0.25=2,7x0,1

a:0,2+a:0,25=0,27

a:0,45=0,27

a=0,27x0,45

a=a,1215

ket qua chuyen a,1215 thanh 0,1215 nhe

a.

\(7^{x+2}+2\times7^{x-1}=345\)

\(7^x\times7^2+2\times7^x\div7=345\)

\(7^x\times\left(7^2+\frac{2}{7}\right)=345\)

\(7^x\times\frac{345}{7}=345\)

\(7^x=345\div\frac{345}{7}\)

\(7^x=345\times\frac{7}{345}\)

\(7^x=7\)

\(x=1\)

b.

\(2^{x+2}-2^x=96\)

\(2^x\times\left(2^2-1\right)=96\)

\(2^x\times3=96\)

\(2^x=\frac{96}{3}\)

\(2^x=32\)

\(2^x=2^5\)

\(x=5\)

\(a,7^{x+2}+2.7^{x-1}=345\Rightarrow7^x.49+\frac{2}{7}.7^x=345\Rightarrow7^x\left(49+\frac{2}{7}\right)=345\Rightarrow7^x.\frac{345}{7}=345\Rightarrow7^x=345:\frac{345}{7}=7^1\Rightarrow x=1\)

\(b,2^{x+2}-2^x=96\Rightarrow2^x.4-2^x=96\Rightarrow2^x\left(4-1\right)=96\Rightarrow2^x.3=96\Rightarrow2^x=96:3=32\Rightarrow2^x=2^5\Rightarrow x=5\)

\(a,7^{x+2}+2.7^{x-1}=345=>7^{x-1+3}+2.7^{x-1}=345=>7^{x-1}.7^3+2.7^{x-1}=345\)

\(=>\left(7^3+2\right).7^{x-1}=345=>345.7^{x-1}=345=>7^{x-1}=1=7^0=>x-1=0=>x=1\)

\(b,2^{x+2}-2^x=96=>2^x.2^2-2^x=96=>2^x.\left(4-1\right)=96=>2^x.3=96=>2^x=32=2^5=>x=5\)