Question

Tìm x, biết rằng :

\(a) 3^{x}+3^{x+2}=810\)

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

Các bạn giúp mình với ! Thanks nha !

Answer 1

a) \(3^x+3^{x+2}=810\)

\(=>3^x+3^x\cdot9=810\)

\(=>3^x\left(1+9\right)=810\)

\(=>3^x\cdot10=810\)

\(=>3^x=810:10=81\)

\(=>3^x=3^4\)

\(=>x=4\)

Answer 2

a) \(3^x+3^{x+2}=810\)

\(\Leftrightarrow3^x\left(1+3^2\right)=810\)

\(\Leftrightarrow3^x\cdot10=810\)

\(\Leftrightarrow3^x=81\)

\(\Leftrightarrow x=4\)

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

\(\Leftrightarrow2^x\left(1+2^3\right)=144\)

\(\Leftrightarrow2^x\cdot9=144\)

\(\Leftrightarrow2^x=16\)

\(\Leftrightarrow x=4\)

Answer 3

a) \(3^x+3^{x+2}=810\)

\(\Rightarrow3^x+3^x.3^2=810\)

\(\Rightarrow3^x.\left(1+3^2\right)=810\)

\(\Rightarrow3^x.10=810\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

Vậy x = 4

b) \(2^x+2^{x+3}=144\)

\(2^x+2^x.2^3=144\)

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

\(2^x.9=144\)

\(2^x=144:9\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

Vậy x = 4

 

Answer 4

b) \(2^x+2^{x+3}=144\)

\(=>2^x+2^x\cdot8=144\)

\(=>2^x\cdot\left(1+8\right)=144\)

\(=>2^x\cdot9=144\)

\(=>2^x=144:9=16\)

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

\(=>x=4\)

Answer 5

a)3^x+3^x+2=810

   3^x.1+3^x.3²=810

    3^x.(1+3²)=810

    3^x.10=810

    3^x=81=3

Vậy x=4

b)2^x+2^x+3=144

    2^x.1+2^x.2³=144

   2^x.(1+2³)=144

   2^x.9=144

   2^x=16=2⁴

Vậy x=4