datgeni5quc

2023-02-23

If $9+\left(81{\right)}^{x}=1/{27}^{x}-3$, find x.

Rigoberto Gordon

$9×{81}^{x}=1/{27}^{x}-3$
${3}^{2}×{3}^{4x}=\left(1/3{\right)}^{3}\left(x-3\right)$
${3}^{2}+4x={3}^{-}\left[3\left(x-3\right)\right]$
Bases are equal. Exponents must be equal.
$2+4x=-\left(3x-9\right)$
2+4x = -3x+9
4x+3x = 9-2
7x = 7
x = 7/7
x = 1
Thus, the value of x is 1

Do you have a similar question?