Problems from Solving an exponential equation by reducing to an equal base

Development:

$3^{x+2}+3^{x+1}\cdot 3^x+3^{x-1}=120$

Extracting common factor of $3^x$ we get $$9\cdot 3^x+3\cdot 3^x+3^x+{\displaystyle \frac{3^x}{3}}=120$$ multiplying by $3$ one has $$27\cdot 3^x+9\cdot 3^x+3\cdot 3^x+3^x=360\Rightarrow 3^x(27+9+3+1)=360\Rightarrow 3^x={\displaystyle \frac{360}{40}}\Rightarrow$$ $$\Rightarrow 3^x=9\Rightarrow x=2$$

Solution:

$x=2$

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