\(3^{-1}.3^n+5.3^{n-1}=162\)

\(\Rightarrow3^{n-1}+5.3^{n-1}=162\)

\(\Rightarrow3^{n-1}\left(1+5\right)=162\)

\(\Rightarrow3^{n-1}.6=162\)

\(\Rightarrow3^{n-1}=162:6=27\)

\(\Rightarrow3^{n-1}=3^3\)

\(\Rightarrow n-1=3\)

\(\Rightarrow n=4\)

\(3.3^{x-2}+5.3^{x-1}=162\)

\(\Rightarrow3^{x-1}+5.3^{x-1}=162\)

\(\Rightarrow3^{x-1}.6=162\)

\(\Rightarrow3^{x-1}=27=3^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=4\)

\(3\cdot3^{x-2}+5\cdot3^{x-1}=162\) 

\(3^{x-1}+5\cdot3^{x-1}=162\) 

\(3^{x-1}\left(5+1\right)=162\) 

\(3^{x-1}\cdot6=162\) 

\(3^{x-1}=27\)  

\(3^{x-1}=3^3\) 

\(x-1=3\) 

\(x=4\) 

Bài làm :

\(3.3^{x-2}+5.3^{x-1}=162\)

\(3^{x-1}+5.3^{x-1}=162\)

\(3^{x-1}\left(1+5\right)=162\)

\(3^{x-1}.6=162\)

\(3^{x-1}=27\)

\(3^{x-1}=3^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=4\)

Học tốt

a)Ta có:(9/25)ⁿ=(3/5)⁴=>(9/25)ⁿ=(9/25)²=>n=2

b)(2ⁿ-2)²=16=>2ⁿ-2=4 hoặc 2ⁿ-2= -4=>2ⁿ=6 hoặc 2ⁿ=-2=>không tìm được giá trị của n thỏa mãn

c)(1-n )³=216=>(1-n)³=6³=>1-n=6=>n=-5

dung ko ban 

3^x-1+5.3^x-1=162

=>3^x-1.6=162

=>3^x-1=162:6

=>3^x-1=27=3³

=>x-1=3

=>x=4

3x+2\(\sqrt{162+n}\)+5(n+3)=0

ĐKXĐ: n \(\ge\) -162

<=>3x=-2\(\sqrt{162+n}\)-5(n+3)

x<-3n-9

=>3x<-9n-27

=>-9n-27>-2\(\sqrt{162+n}\)-5(n+3)

<=>9n+27>2\(\sqrt{162+n}\)+5(n+3)

<=>4n+12>2\(\sqrt{162+n}\)

<=>2n+6>\(\sqrt{162+n}\)

ĐK có nghiệm: n\(\ge\)-3

<=>4n²+24n+36>162+n

<=>4n²+23n-126>0

<=>\(\dfrac{-23+\sqrt{2545}}{8}< n\)hoặc n<\(\dfrac{-23-\sqrt{2545}}{8}\)

Vậy...

a, 5ⁿ+5ⁿ⁺²=650

=>5ⁿ+5ⁿ.5²=650

=>5ⁿ(1+25)=650

=>5ⁿ.26=650

=>5ⁿ=25

=>5ⁿ=5²

=>n=2

 Vậy n=2

Có 3^n+1-3^n=3^n.3-3^n=3^n(3-1)=3^n.2

Suy ra 3^n.2=162

3^n=162:2=81

3^n=3^4.Suy ra n = 4

3^n-1+5.3^n-1=162

3^n-1.(5+1)=162

3^n-1.6=162

3^n-1=162:6

3^n-1=27=3³

=>n-1=3

=>n=3+1

=>n=4

5ⁿ+5ⁿ⁺²=650

5ⁿ+5ⁿ.5²=650

5ⁿ.(5²+1)=650

5ⁿ.26=650

5ⁿ=650:26

5ⁿ=25=5²

=>n=2

a, n =4

b, n=2