Question

\(3^x+3^{x+2}+3^{x+4}=2457\)

Answer 1

\(3^x+3^{x+2}+3^{x+4}=2457\)

\(\Leftrightarrow3^x+3^2.3^x+3^4.3^x=2457\)

\(\Leftrightarrow3^x.\left(1+3^2+3^4\right)=2457\)

\(\Leftrightarrow3^x.91=2457\)

\(\Leftrightarrow3^x=2457:91\)

\(\Leftrightarrow3^x=27=3^3\)

\(\Leftrightarrow x=3\)

Answer 2

\(3^x+3^{x+2}+3^{x+4}=2457\)

\(\Leftrightarrow3^x+3^x.9+3^x.81=2457\)

\(\Leftrightarrow3^x\left(1+9+81\right)=2457\)

\(\Leftrightarrow3^x.91=2457\)

\(\Leftrightarrow3^x=27\Leftrightarrow3^x=3^3\Leftrightarrow x=3\)