(3*3^n-1)*((6*3^n+2)+3)-(2*3^n)*((3^n+3)-1)=405 Tìm "n"

\(3.3^{n-1}(6.3^{n+2}+3)-2.3^n(3^{n+3}-1)=405\)

\(\Leftrightarrow 3^n(6.9.3^n+3)-2.3^n(27.3^n-1)=405\)

\(\Leftrightarrow 54.3^{2n}+3.3^n-54.3^{2n}+2.3^n=405\)

\(\Leftrightarrow 5.3^n=405\)

\(\Leftrightarrow3^n=81\)

\(\Leftrightarrow 3^n=3^4\)

\(\Leftrightarrow n=4\).

Đáp án:

Giải thích các bước giải:

$ \color {Indigo blue } { (3 \times 3 ^ n  - 1) ( (6 \times 3 ^ n + 2 ) + 3) - (2 \times 3 ^ n ) ( (3 ^ n + 3) - 1) = 405 \\\Leftrightarrow -410 + 5\cdot 3^{n} + 16\cdot 3^{2\,n}} = 0 \\\Leftrightarrow x = 1,448120128$