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Giải thích các bước giải:

Đặt $A=3^{x+1}+3^{x+2}+...+3^{x+50}$

$\to 3A= 3^{x+2}+3^{x+3}+...+3^{x+51}$

$\to 3A-A=3^{x+51}-3^{x+1}$

$\to 2A=3^{x+51}-3^{x+1}$

$\to A=\dfrac{3^{x+51}-3^{x+1}}2$

$\to \dfrac{3^{x+51}-3^{x+1}}2=\dfrac{3^{54}-81}2$

$\to 3^{x+51}-3^{x+1}=3^{54}-81$

$\to 3^{x+51}-3^{x+1}=3^{54}-3^4$

$\to 3^{x+1}\cdot (3^{50}-1)=3^4\cdot (3^{50}-1)$

$\to 3^{x+1}=3^4$

$\to x+1=4$

$\to x=3$