Question

Exercițiul 3, vă rog este urgent!! Mulțumescc , ofer COROANĂ.

Answer 1

 

$\displaystyle\\3^x+3^{x+2}=10\\\\3^x+3^x\cdot3^2}=10\\\\3^x\Big(1+3^2\Big)=10\\\\3^x\Big(1+9\Big)=10\\\\10\cdot3^x=10\\3^x=\frac{10}{10}\\\\3^x=1\\\\\boxed{x=0}\\\\\text{Verificare:}\\\\3^0+3^{0+2}=3^0+3^2=1+9=10~~~~\text{(Corect)}$

Answer 2

3ˣ⁺²=3ˣ*3²

3ˣ+3ˣ⁺²=3ˣ+3ˣ*3²=3ˣ(1+3²)

3ˣ+3ˣ⁺²=10=>3ˣ(1+3²)=10=>3ˣ=10/(1+3²)=10/10=1=>3ˣ=1=>3ˣ=3⁰=>(injectivitatea functiei exponentiale):x=0