\(27^n:3^n=\left(27:3\right)^n=9\)

\(9^n=9\rightarrow n=1\)

\(\left(\frac{25}{5}\right)^n=5^n=5^1\)

\(\rightarrow n=1\)

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

\(\rightarrow\left(-3\right)^n=81:\left(-3\right)^5=\frac{-1}{3}=\left(-3\right)^{-1}\)

\(\)

a: =>9^n=9

=>n=1

b: =>5^n=5

=>n=1

c: \(\Leftrightarrow\left(-27\right)^n=-243\)

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

=>3n=5

=>n=5/3

d: =>2^n*9/2=9*2^5

=>2^n=9*2^5:9/2=2^5*2=2^6

=>n=6

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

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

   \(2^n.\frac{9}{2}=3^2.5^n\)

a)n=1

b)n=4

c)n=1

d)n=6

e)n=-1

a) Câu này thiếu đề nhé bạn.

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

\(\Rightarrow5^n=25:5\)

\(\Rightarrow5^n=5\)

\(\Rightarrow5^n=5^1\)

\(\Rightarrow n=1\)

Vậy \(n=1.\)

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

\(\Rightarrow\left(-3\right)^n=81:\left(-243\right)\)

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

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

\(\Rightarrow n=-1\)

Vậy \(n=-1.\)

e) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)

\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)

\(\Rightarrow n=4\)

Vậy \(n=4.\)

f) \(\left(-\frac{3}{4}\right)^n=\frac{81}{256}\)

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

\(\Rightarrow n=4\)

Vậy \(n=4.\)

Chúc bạn học tốt!

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

\(\Rightarrow2^n.\left(\frac{1}{2}+4\right)=288\)

\(\Rightarrow2^n.\frac{9}{2}=288\)

\(\Rightarrow2^n=288:\frac{9}{2}\)

\(\Rightarrow2^n=64\)

\(\Rightarrow2^n=2^6\)

\(\Rightarrow n=6\)

Vậy \(n=6.\)

g) \(-\frac{512}{343}=\left(-\frac{8}{7}\right)^n\)

\(\Rightarrow\left(-\frac{8}{7}\right)^n=\left(-\frac{8}{7}\right)^3\)

\(\Rightarrow n=3\)

Vậy \(n=3.\)

h) \(5^{-1}.25^n=125\)

\(\Rightarrow5^{-1}.5^{2n}=5^3\)

\(\Rightarrow5^{-1+2n}=5^3\)

\(\Rightarrow-1+2n=3\)

\(\Rightarrow2n=3+1\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=4:2\)

\(\Rightarrow n=2\)

Vậy \(n=2.\)

k) \(3^{-1}.3^n+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}.\left(1+6\right)=7.3^6\)

\(\Rightarrow3^{n-1}.7=7.3^6\)

\(\Rightarrow n-1=6\)

\(\Rightarrow n=6+1\)

\(\Rightarrow n=7\)

Vậy \(n=7.\)

Chúc bạn học tốt!

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

\(5^n\)=25/5

\(5^n\)=\(5^1\)

⇒ n = 1

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

\(\left(-3\right)^n\)=81/-243

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

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

⇒n=-1

b, \(2^n\left(2^{-1}+4\right)=9\cdot2^5\)

=> \(2^n\cdot\frac{9}{2}=9\cdot2^5\)

=> \(2^n=2^6\)

Vậy \(n=6\left(tm\right)\)

a, \(A=4\cdot16\cdot\frac{9}{16}\cdot\frac{4}{5}\cdot\frac{27}{8}=\frac{486}{5}=97,2\)

a) 

\(A=\left(0,25\right)^{-1}\cdot\left(\frac{1}{4}\right)^{-2}\cdot\left(\frac{4}{3}\right)^{-2}\cdot\left(\frac{5}{4}\right)^{-1}\cdot\left(\frac{2}{3}\right)^{-3}\)

\(A=4\cdot16\cdot\frac{9}{16}\cdot\frac{4}{5}\cdot\frac{27}{8}=\frac{4\cdot16\cdot9\cdot4\cdot27}{16\cdot5\cdot8}=\frac{9\cdot2\cdot27}{5}=\frac{486}{5}\)

b)

2^-1.2ⁿ+4.2ⁿ=9.2⁵

(1/2+4).2ⁿ=288

2ⁿ=288:(1/2+4) =64

=>2ⁿ=2⁶

=> n = 6

a) \(8< 2^x\le2^9.2^{-5}\)

\(\Leftrightarrow2^3< x\le2^{9-5}\)

\(\Leftrightarrow2^3< 2^x\le2^4\)

\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)

b) \(27< 81^3:3^x< 243\)

\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)

\(\Leftrightarrow2< 12-x< 5\)

\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)

a,\(8< 2^x\le2^9.2^{-5}\)

\(2^3< 2^x\le2^4\)

\(\Rightarrow x=4\)

b, \(27< 81^3.3^x< 243\)

\(3^3< 3^{12-x}< 3^5\)

\(\Rightarrow3< 12-x< 5\)

12-x=4

x=8

c,\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^3.\left(\frac{2}{5}\right)^2\)

\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^5\)

\(\Rightarrow x>5\)

x=6;7;8........

tìm x, biết:

(5x+1)^2=36/49