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

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

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

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

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

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

5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha

b) Ta có :

n³⁵ : n³² = 64

n³ = 64

4³ = 64

=> n = 4

\(b,\text{ }n^{35}\text{ : }n^{32}=64\)

\(n^3=64\)

\(n^3=4^3\)

\(\Rightarrow\text{ }n=4\)

\(c,\text{ }49\cdot7^{2n+3}=2401\cdot343\)

\(7^2\cdot7^{2n+3}=7^4\cdot7^3\)

\(7^{2n+3+2}=7^7\)

\(7^{2n+5}=7^7\)

\(\Rightarrow\text{ }2n+5=7\)

\(2n=7-5\)

\(2n=2\)

\(n=2\text{ : }2\)

\(n=1\)

\(b,\text{ }n^{35}\text{ : }n^{32}=64\)

\(n^3=64\)

\(n^3=4^3\)

\(\Rightarrow\text{ }n=4\)

\(c,\text{ }49\cdot7^{2n+3}=2401\cdot343\)

\(7^2\cdot7^{2n+3}=7^4\cdot7^3\)

\(7^{2n+3+2}=7^7\)

\(7^{2n+5}=7^7\)

\(\Rightarrow\text{ }2n+5=7\)

\(2n=7-5\)

\(2n=2\)

\(n=2\text{ : }2\)

\(n=1\)

a,  \(\frac{8}{2^n}=2\Rightarrow2.2^n=8\)

                     \(\Rightarrow2^{n+1}=2^3\)

                     \(\Rightarrow n+1=3\)

                      \(\Rightarrow n=2\)

d,\(\left(2n-3\right)^2=9\)

\(\left(2n-3\right)^2=3^2\)

\(\Rightarrow\orbr{\begin{cases}2n-3=-3\\2n-3=3\end{cases}\Rightarrow\orbr{\begin{cases}2n=-3+3\\2n=3+3\end{cases}\Rightarrow}\orbr{\begin{cases}2n=0\\2n=6\end{cases}\Rightarrow}\orbr{\begin{cases}n=0\\n=3\end{cases}}}\)

      Vậy n=0; n= 3

TL:

a.\(2^6.2^n=2^{11}\) 

 \(2^{6+n}=2^{11}\) 

\(\Rightarrow n=5\) 

b. \(3^7:3^n=3^4\) 

  \(3^{7-n}=3^4\) 

\(\Rightarrow n=3\) 

c.\(2^n.32=2^{10}\)

 \(2^{n+5}=2^{10}\) 

\(\Rightarrow n=5\) 

a: =>2x^3=58-4=54

=>x^3=27

=>x=3

b; =>(5-x)^5=2^5

=>5-x=2

=>x=3

c: =>(5x-6)^3=4^3

=>5x-6=4

=>5x=10

=>x=2

d: (3x)^3=(2x+1)^3

=>3x=2x+1

=>x=1

1=>2x³=54
=>x³=27  =>x=3
2=>(5-x)⁵=2⁵
=>5-x=2
=>x=3
3=>(5x-6)³=4³
=>5x-6=4
=>5x=10=>x=2
4=>3x=2x+1
=>x=1

\(=9^n-9^n-1\cdot3+1\cdot3^n=3^n-3\)