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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a) (2n-1)⁴ : (2n-1) = 27

(2n-1)³ = 27  =3³

=> 2n - 1= 3

=> 2n = 4

n = 2

phần b,c làm tương tự nha bn

d) (21+n) : 9 = 9⁵:9⁴

(2n+1) : 9 = 9

2n + 1 = 81

2n = 80

n = 40

Tìm số tự nhiên n, biết :

a/ (2.n−1)4:(2.n−1)=27

\(\left(2.n-1\right)^3=27\)

\(2.n-1=3^3\Rightarrow2.n-1=3\)

2.n - 1 = 3

2.n      = 3 + 1

   n      =  4 : 2

   n      =  2

B,C tương tự nha

d) \(\left(21+n\right):9=9^5:9^4\)

   \(\left(21+n\right):9=9\)

        \(21+n=9.9\)

         \(21+n=81\)

                 \(n=81-21\)

                  \(n=60\)

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{n\left(n+1\right)}=\frac{2}{9}\)

\(\frac{1}{2}\left(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{n\left(n+1\right)}\right)=\frac{2}{9}.\frac{1}{2}\)

\(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+....+\frac{1}{n\left(n+1\right)}=\frac{1}{9}\)

\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{n\left(n+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{n+1}=\frac{1}{9}\)

\(\frac{1}{n+1}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{n+1}=\frac{1}{18}\)

\(\Rightarrow n+1=18\)

\(\Rightarrow n=17\)

Xét công thức: 1+2+3+.....+n = n(n+1):2

1+2+.....+n = 36

=> n(n+1) : 2 = 36

=> n(n+1) = 36 x 2 = 72

Mà n(n+1) =8 x (8+1)

Vậy n = 8

1.67365

2.48

3.3927

4.có

các bạn giải giúp mình với

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Tớ chịu thua! tk nha

a) \(\left(\frac{1}{3}\right)^n=\frac{1}{27}\)

\(\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^3\)

\(\Rightarrow n=3\)

b) \(\left(\frac{3}{5}\right)^n=\frac{81}{625}\)

\(\left(\frac{3}{5}\right)^n=\left(\frac{3}{5}\right)^4\)

\(\Rightarrow n=4\)

c) \(3^n\cdot2^n=36\)

\(\left(3\cdot2\right)^n=36\)

\(6^n=6^2\)

\(\Rightarrow n=2\)

d) \(\frac{2^n}{3^n}=\frac{8}{27}\)

\(\left(\frac{2}{3}\right)^n=\left(\frac{2}{3}\right)^3\)

\(\Rightarrow n=3\)

giúp tui với 

tui đang cần lắm đó bà con ơi

em mới lớp 5 seo anh gọi em là: BÀ CON

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