Question

Tìm x:

\(4.3^{x+2}-3^{x-1}=963\)

Giúp e với

Answer 1

\(4.3^{x+2}-3^{x-1}=963\)

\(\Rightarrow4.3^{x+2}-3^{x+2-3}=963\)

\(\Rightarrow4.3^{x+2}-\dfrac{1}{3^3}3^{x+2}=963\)

\(\Rightarrow4.3^{x+2}-\dfrac{1}{27}3^{x+2}=963\left(1\right)\)

Đặt \(t=3^{x+2}>0\)

\(\left(1\right)\Rightarrow4t-\dfrac{1}{27}t=963\)

\(\Rightarrow t\left(4-\dfrac{1}{27}\right)=963\)

\(\Rightarrow\dfrac{107}{27}.t=9.107\)

\(\Rightarrow t=3^2\Rightarrow t=3^2:\dfrac{1}{3^3}=3^2.\dfrac{3^3}{1}=3^5\)

\(\Rightarrow3^{x+2}=3^5\Rightarrow x+2=5\Rightarrow x=3\)

Answer 2

4\(\cdot\)3^x+2-3^x-1=963

=>4\(\cdot\)3^xx3²-3^x:3=963

=>3^x\(\cdot\)36-3^x\(\cdot\)\(\dfrac{1}{3}\)=963

=>3^x\(\cdot\)(36-\(\dfrac{1}{3}\))=963

=>3^x\(\cdot\)\(\dfrac{107}{3}\)=963

=>3^x=963:\(\dfrac{107}{3}\)=27=3³

=>x=3