Bài 2

a) x=5

b)x=1

Bạn ghi lại đề bằng công thức đi bạn

Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

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sao khong ai tra loi het  z troi - .-

3^x*5^x-1=224

3^x*5^x/5=224

15^x=224*5

15^x=1120

=>ko tồn tại x thỏa mãn đề bài vị 15^x luôn có tận cùng bằng 5 (x khác 0 ) hoặc 1 ( x=0) ma 1120 co tận cùng bằng 0

1) \(2^x-15=17\)

\(\Leftrightarrow2^x=32=2^5\)

\(\Rightarrow x=5\)

2) \(\left(7x-11\right)^3=25\cdot5^2+200\)

\(\Leftrightarrow\left(7x-11\right)^3=825\)

\(\Leftrightarrow7x-11=\sqrt[3]{825}\)

\(\Leftrightarrow7x=11+\sqrt[3]{825}\)

\(\Rightarrow x=\frac{11+\sqrt[3]{825}}{7}\)

3) \(\left(x+1\right)^{100}-3\left(x+1\right)^{99}=0\)

\(\Leftrightarrow\left(x+1\right)^{99}\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x+1\right)^{99}=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

4) \(4x+5\left(x+3\right)=105\)

\(\Leftrightarrow9x+15=105\)

\(\Leftrightarrow9x=90\)

\(\Rightarrow x=10\)

5) \(5\cdot\left(x-2\right)+10\left(x+3\right)=170\)

\(\Leftrightarrow5\left[x-2+2\left(x+3\right)\right]=170\)

\(\Leftrightarrow3x+4=34\)

\(\Leftrightarrow3x=30\)

\(\Rightarrow x=10\)

cảm ơn bạn nhá NGUYỄN MINH ĐĂNG

giúp mình với

1)1/9 x 3^x = 2187:81=27

            3^x=27:1/9=243=3⁵

            =>x=5

\(\frac{1}{9}.3^4.3^x=3^7\)

\(\Leftrightarrow3^x=3^7:\frac{1}{9}:3^4=243\)

\(\Leftrightarrow3^x=3^5\)

\(\Leftrightarrow x=5\)

a) 25+x=0

   x=0-25

  x=-25

b)\(2^x:2^{19}=2^{25}\)

\(2^x=2^{25}.2^{19}\)

\(2^x=2^{44}\)

=>x=44

c)\(5^x.5^{18}=5^{54}\)

\(5^x=5^{54}:5^{18}\)

\(5^x=5^{36}\)

=>x=36

TL :

a) \(25+x=0\)

\(x=0-25\)

\(x=-25\)

b) \(2^x:2^{19}=2^{35}\)

\(2^x=2^{25}.2^{19}\)

\(2^x=2^{44}\)

\(\Rightarrow x=44\)

c) \(5^x.5^{18}=5^{54}\)

\(5^x=5^{54}:5^{18}\)

\(5^x=5^{36}\)

\(\Rightarrow x=36\)

Học tốt

a,25+x=0

\(\Rightarrow\)x= 0-25

\(\Rightarrow\)x= -25

Vậy x=-25

b, 2\(^x\): 2\(^{19}\)=2\(^{25}\)

\(\Rightarrow\)2\(^x\)= 2\(^{25}\). 2\(^{19}\)= 2\(^{25+19}\)

\(\Rightarrow\)2\(^x\)= 2\(^{44}\)

\(\Rightarrow\)x = 44

Vậy x=44

c, 5\(^x\). 5\(^{18}\)= 5\(^{54}\)

5\(^x\)= 5\(^{54}\): 5\(^{18}\)= 5\(^{54-18}\)

\(\Rightarrow\)5\(^x\)= 5 \(^{36}\)

\(\Rightarrow\)x= 36

vậy x = 36