\(3x-2+5.3x+1=408\)

\(3x-2+15x+1=408\)

\(18x-1=408\)

\(18x=409\)

\(x=\frac{409}{18}\)

vậy \(x=\frac{409}{18}\)

3x - 2 + 5.3x + 1 = 408

3x - 2 + 15x +1 = 408

(3x + 15x) - (2 - 1) = 408

18x - 1 = 408

18x = 408 + 1

18x = 409

x = 409 : 18

x = 22,7(2)

3x-2+5*3x+1=408

3x-2+15x+1=408

(3x+15x)-2+1=408

18x-2+1=408

18x-2=408-1=407

18x=407+2=409

Suy ra(dung dau suy ra nhé) x=409:18=409/18

Trường hợp 1 :

2.3^x + 5.3^x+1 = 153

=> 2.3^x + 5.3^x + 3 = 153

=> (2 + 5).3^x = 150

=> 7.3^x = 150 

=> 3^x = 150/7 => x không thỏa mãn

Trường hợp 2 :

2.3^x + 5.3^x + 1 = 153

=> (2 + 5).3^x = 152

=> 7 . 3^x = 152

=> 3^x= 152/7 => x không thỏa mãn

Nếu bạn không gõ latex thì 2 trường hợp cũng sẽ xảy ra :((

a) 3^{x + 2} + 5.3^{x + 1} = 648

<=> 3^{x + 1}.8 = 648

<=> 3^{x + 1} = 81

<=> 3^{x + 1} = 3⁴ 

<=> x + 1 = 4

<=> x = 3

Sửa lại đề: b) 2^{2x + 1}  + 2^{2x + 4} = 3².8⁴

<=> 2^{2x + 1}.9 = 3² . 8⁴ 

<=> 2^{2x + 1} = 8⁴ 

<=> 2^{2x + 1}  = 2¹² 

<=> 2x + 1 = 12 

<=> \(x=\dfrac{11}{2}\)

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

\(2^{x+2}-2^x=96\)

\(\Rightarrow2^x\cdot2^2-2^x=96\)

\(\Rightarrow2^x\left(2^2-1\right)=96\)

\(\Rightarrow2^x\left(4-1\right)=96\)

\(\Rightarrow2^x\cdot3=96\)

\(\Rightarrow2^x=96:3\)

\(\Rightarrow2^x=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

\(5^x+5^{x+1}=750\)

\(\Rightarrow5^x+5^x\cdot5=750\)

\(\Rightarrow5^x\left(1+5\right)=750\)

\(\Rightarrow5^x\cdot6=750\)

\(\Rightarrow5^x=750:6\)

\(\Rightarrow5^x=125\)

\(\Rightarrow5^x=5^3\)

\(\Rightarrow x=3\)

\(2^{x+3}+2^x=144\)

\(\Rightarrow2^x\cdot2^3+2^x=144\)

\(\Rightarrow2^x\left(2^3+1\right)=144\)

\(\Rightarrow2^x\cdot9=144\)

\(\Rightarrow2^x=144:9\)

\(\Rightarrow2^x=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)