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

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

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

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

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

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

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

\(\Rightarrow x-1=3\)

\(x=3+1\)

\(x=4\)

Vậy \(x=4\)

Ý bạn là \(\left(3^x-1+5\right)\left(3^x-1\right)\)

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

\(3^{x-1+5}\) hay là \(3^{x-1}+5\) hay là \(3^x-1+5\) thế bạn

Lời giải:

$3^{-1}.3^x+5.3^{x-1}=162$

$3^{x-1}+5.3^{x-1}=162$

$3^{x-1}(1+5)=162$

$3^{x-1}.6=162$

$3^{x-1}=27=3^3$

$\Rightarrow x-1=3$

$\Rightarrow x=4$

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

<=>3^x-1.(1+5)=162

=>3^x-1.6=162

=>3^x-1=162:6

=>3^x-1=27

=>3^x-1=3³

=>x-1=3

=>x=3+1

=>x=4

Chúc bạn học giỏi nha!!!

K cho mik với nhé Nguyễn Trần Thanh Vy

3^X-1 + 5 * 3^X-1 = 162

3^X-1 *  (5+1) = 162

3^X-1 * 6 = 162

3^X-1 = 27

=> 3^X-1 = 3³

=>X-1=3

=>X=4

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

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

3^x-1.6=162

3^x-1=162:6

3^x-1=27

3^x-1=3³

=)x-1=3

=)x=3-1

=)x=2

a)5^x+5^x+2=650

2*5^x+2=650

2(5^x+1)=650

5^x+1=650/2

5^x+1=325

5^x=325-1

5^x=324

=>x \(\in\phi\)

b)3^x-1+5*3^x-1=162

3^x-1(1+5)=162

3^x-1=162/6

3^x-1=27=3³

=>x-1=3

x=3+1

x=4

c)(2x-1)⁶=(1-2x)⁸

(2x-1)⁶=(-2x-1)⁸=(2x-1)⁸=(2x-1)⁶*(2x-1)²

=>(2x-1)²=1

2x-1=1

2x=1+1

2x=2

x=2/2

x=1

*)2x-1=0

2x=0+1

2x=1

x=1/2

102,5m2

3^n-1 + 5.3^n-1 = 162

3^n-1.6 = 162

3^n-1 = 27 = 3³

=> n-1 = 3

n = 4

3^{n - 1} + 5.3^{n - 1} = 162

=> 3^{n - 1}(1 + 5) = 162

=> 3^{n - 1}.6 = 162

=> 3^{n - 1} = 27

=> 3^{n - 1} = 3³

=> n - 1 = 3

=> n = 2

vậy_

n = 2

hoặc n = 4

ko đúng thì thôi nha :)

3^x-1.6 = 162

3^x-1 = 27

3^x-1 = 3³

=> x - 1 = 3

x = 4

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

=>3^x-1.(1+5)=162

=>3^x-1.6=162=>3^x-1=162:6=27=3³

=>x-1=3=>x=4

5^x+5^x+2=650

=>5^x+5^x.5²=650

=>5^x.(1+25)=650

=>5^x.26=650=>5^x=650:26=25=5²

=>x=2