aⁿ= 1

=> n = 0

Vậy n = 0

     x⁵⁰= x

=> x\(\in\left\{0;1\right\}\)

n=0  ;   x=1

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

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

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

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

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

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

a/ 2ⁿ = 16 

Vì 2.2.2.2 = 16 

=> n = 4

b/ 4ⁿ = 64

Vì 4.4.4 = 64 

=> n = 3

c/ 15ⁿ = 225

Vì 15 . 15 = 225

=> n = 2

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\(a,2^n=16\Leftrightarrow2^n=2^4\Leftrightarrow n=4\)

\(3^n=243\Rightarrow3^n=3^5\Leftrightarrow n=5\)

\(b,4^n=4096\Rightarrow4^n=4^6\Leftrightarrow n=6\)

\(5^n=15625\Rightarrow5^n=5^6\Leftrightarrow n=6\)

\(c,6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Leftrightarrow n=0\)

\(4^{n-1}=1024\Rightarrow4^{n-1}=4^5\Rightarrow n-1=5\Leftrightarrow n=6\)

\(a.\)  \(2^n=16\Rightarrow2^n=2^4\Leftrightarrow n=4\)

        \(3^n=243\Rightarrow3^n=3^5\Leftrightarrow n=5\)

\(b.\)   \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)

           \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)

\(c.\)   \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)

         \(4^{n-1}=1024\Rightarrow4^{n-1}=4^5\Rightarrow n-1=5\Rightarrow n=6\)

a) \(11^n=1331\)

\(\Rightarrow11^n=11^3\)

\(\Rightarrow n=3\)

b) \(n^3=125\)

\(\Rightarrow n^3=5^3\)

\(\Rightarrow n=5\)

c) \(5^4=n\)

\(\Rightarrow625=n\)

\(\Rightarrow n=625\)

d) \(\left(n+1^2\right)=9\)

\(\Rightarrow n+1=9\)

\(\Rightarrow n=9-1\)

\(\Rightarrow n=8\)

a) 11^n = 1331

⇒ 11^n = 11^3

⇔ n = 3

b) n^ 3 = 125

⇒ n^3 = 5^3

⇔ n = 5

c) 5^4 = n 

⇒ n = 625

d) ( n + 1^2 ) = 9

⇒ ( n + 1 ) = 9

⇒ n = 8 

a) n = 4

b) n = 3

c) n= 2

a, 2^n= 16

2^n= 2^4

=> n=4

b, 4^n= 64

4^n= 4^3

=> n=3

c, 15^n =225

15^n= 15^2

=> n=2