a)27ⁿ:3ⁿ=9

   (27:3)ⁿ=9

   9ⁿ=9¹

   n=1

Vậy n=1

b)\(\left(\frac{25}{5}\right)^n=5\)

    \(5^n=5^1\)

    n=1

Vạy n=1

c)\(\left(-\frac{81}{3}\right)^n=-243\)

   \(\left(-27\right)^n=\left(-3\right)^5\)

   \(\left[\left(-3\right)^3\right]^n=\left(-3\right)^5\)

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

    \(3n=5\)

   \(n=\frac{5}{3}\)

Vậy \(n=\frac{5}{3}\)

d)\(\frac{1}{2}.2^n+4.2^n=9.5^n\)

   \(2^n.\left(\frac{1}{2}+4\right)=9.5^n\)

   \(2^n.\frac{9}{2}=3^2.5^n\)

Mk làm lun, ko viết lại đề bài nữa nhé =))

a) \(\Leftrightarrow\)\(3^2.3^{n+1}=9^4\)

\(\Leftrightarrow3^{n+1}=9^4:3^2\)

\(\Leftrightarrow3^{n+1}=3^6\)

\(\Rightarrow n+1=6\)

\(\Leftrightarrow n=6-1\)

\(\Rightarrow n=5\)

b)\(\Leftrightarrow2^n.\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)

\(\Rightarrow2^n=\left(9.2^5\right):\frac{9}{2}\)

\(\Rightarrow2^n=468:\frac{9}{2}\)

Tự tính nốt KQ giúp mk nha ♥

a)1/9*3⁴*3ⁿ⁺¹=9⁴

3⁴*3ⁿ⁺¹ =9⁴/(1/9)=9⁴*9=9⁵

3⁴*3ⁿ⁺¹=3⁴⁺ⁿ⁺¹=9⁵=(3²)⁵=3¹⁰

=>4+n+1=10

n=10-4-1

Vậy n=5

b)1/2*2ⁿ+4*2ⁿ=9*2⁵

2ⁿ*(1/2+4)=9*2⁵

2ⁿ*4.5=9*2⁵

2ⁿ=9*2⁵/4.5=2⁵*2=2⁶

=> Vậy n=6

\(a)\frac{1}{9}.3^4.3^{n+1}=9^4\)

\(\Rightarrow3^{-2}.3^4.3^{n+1}=3^8\)

\(\Rightarrow3^{-2+4+n+1}=3^{n+3}=3^8\)

\(\Rightarrow n+3=8\Rightarrow n=5\)

\(b)\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}=\frac{9.2^5.2}{9}=2^6\)

\(\Rightarrow n=6\)

a) 27^n : 3^n = 9

     (27 : 3)^n  = 9

         9^n        = 9

=> n = 1

b) 25/5^n = 5

       5^n     = 25 : 5

       5^n     = 5

=> n = 1

c) 81/(-3)^n = -243

         (-3)^n   = -243 : 81

         (-3)^n   = -3

=> n = 1

d) 1/2 . 2^n + 4 . 2^n = 9 . 2^5

       2^n . (1/2 + 4)     = 9 . 32

       2^n . 9/2              = 288

       2^n                       = 288 : 9/2

       2^n                       = 64

       2^n                       = 2^6

=> n = 6

thank you for doing your homework well !

\(a)27^n\div3^n=9\)

\(\Rightarrow\left(27\div3\right)^n=9\)

\(\Rightarrow9^n=9\Rightarrow n=1\)

\(b)\frac{25}{5^n}=5\Rightarrow25=5^{n+1}\Rightarrow5^2=5^{n+1}\Rightarrow2=n+1\Rightarrow n=1\)

\(c)\frac{81}{\left(-3\right)^n}=-243\Rightarrow\frac{81}{\left(-3\right)^n}=\left(-3\right)^5\)

\(\Rightarrow81=\left(-3\right)^{n+5}\Rightarrow\left(-3\right)^4=\left(-3\right)^{n+5}\)

\(\Rightarrow4=n+5\Rightarrow n=-1\)

\(d)\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}\Rightarrow2^n=\frac{9.2^5.2}{9}=2^6\)

\(\Rightarrow n=6\)

a: \(\Leftrightarrow3^n:27^n=\dfrac{1}{9}\)

\(\Leftrightarrow\left(\dfrac{1}{9}\right)^n=\dfrac{1}{9}\)

hay n=1

b: \(\Leftrightarrow3^n\cdot3^2=3^8\)

=>n+2=8

hay n=6

c: \(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)

\(\Leftrightarrow2^n=2^6\)

hay n=6

d: \(\Leftrightarrow8^n=512\)

hay n=3

#)Giải :

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

\(\frac{1}{9}.81.3^n=3^7\)

\(9.3^n=3^7\)

\(3^2.3^n=3^7\)

\(\Rightarrow2+n=7\)

\(\Rightarrow n=5\)

       #~Will~be~Pens~#

#)Giải :

\(\frac{1}{9}.27^n=3^n\)

\(\Leftrightarrow\frac{1}{9}=\frac{3^n}{27^n}\)

\(\Leftrightarrow\frac{1}{9}=\left(\frac{1}{9}\right)^n\)

\(\Leftrightarrow n=1\)

         #~Will~be~Pens~#

17/5×1/2×10/17×-1/8

17/10×-10/136

-170/1360

-1/8

5/54+10/63+5/63+15/63

5/54+15/63+15/63

5/54+30/63

315/3402+1620/3402

1935/3402