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

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

=> x-1=3

=> x=3+1

=> x=4

Vậy x=4

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

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

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

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

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

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

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

\(\Rightarrow x-1=3\)

\(x=3+1\)

\(x=4\)

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

3^x-1.6 = 162

3^x-1 = 27

3^x-1 = 3³

=> x - 1 = 3

x = 4

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

th1: \(\left(\frac{y}{3}-5\right)^{2008}-\left(\frac{y}{3}-5\right)^{2000}=0\)

\(\left(\frac{y}{3}-5\right)^{2000}.\left[\left(\frac{y}{3}-5\right)^8-1\right]=0\)

\(=>\orbr{\begin{cases}\left(\frac{y}{3}-5\right)^{2000}=0\\\left(\frac{y}{3}-5\right)^{2008}-1=0\end{cases}}\)

\(=>\orbr{\begin{cases}\frac{y}{3}=5=>y=15\\\frac{y}{3}=6=>y=18,\frac{y}{3}=4=>y=12\end{cases}}\)

Vậy ...

P/S: cái đoạn\(\left(\frac{y}{3}-5\right)^{2008}-1=0\)vì số mũ chẵn nên y=18 hay bằng 12 nha!