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

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

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

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

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

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

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

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

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

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

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

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

a)2^n=16 =>n=4; 3^n=243 =>n=5

b)4^n=4096=>n=6;5^n=15625=>n=6

c)6^n+3=216=>n=0;4^n-1=1024=>n=6

a) \(2^n:4=16\Rightarrow2^n:2^2=2^4\Rightarrow2^{n-2}=2^4\Rightarrow n-2=4\Rightarrow n=6\)

b) \(6\cdot2^n+3\cdot2^n=9\cdot2^9\)

=> \(\left(6+3\right)\cdot2^n=9\cdot2^9\)

=> \(9\cdot2^n=9\cdot2^9\Rightarrow n=9\)

c) \(3^n:3^2=243\)

=> \(3^{n-2}=3^5\)

=> n - 2 = 5 => n = 7

d) 25 < 5ⁿ < 3125

=> 5² < 5ⁿ < 5⁵

=> n \(\in\){3;4}

a,     2^n =32

<=> 2^n  = 2^5

=>       n=5

\(3^5=32\)                       \(n=5\)

n không tồn tại                  n không tồn tại

So sánh

ta có: 243³ < 243¹³

=> \(\frac{1}{243^4}>\frac{1}{243^{13}}\)

#

243:3⁴=3⁵:3⁴=3¹

10⁹:10000=10⁹:10⁴=10⁵

10 mũ 5

Giai

243:3⁴=3⁵:3⁴=3¹

a) 2.16 \(\ge\) 2ⁿ > 4

32 \(\ge\) 2ⁿ > 4

=> n = 3,4 . Tương đương với 2ⁿ = 2³ ; 2ⁿ = 2⁴

b) 9.27 \(\le\) 3ⁿ \(\le\) 243

243 \(\le\) 3ⁿ \(\le\) 243

=> 3ⁿ = 243 = 3⁵ . Tương đương với 3ⁿ=3⁵ , vậy n = 5