Ayaana Buck

2021-02-08

${9}^{x}-1={27}^{-x}+2$

diskusje5

We are given: ${9}^{x}-1={27}^{-x}+2$
Assign a power of 3 to each base: ${\left({3}^{2}\right)}^{x}-1={\left({3}^{3}\right)}^{-x}+2$
Use the rule: ${\left({a}^{m}\right)}^{n}={a}^{m}n$ ${3}^{2}\left(x-1\right)={3}^{{2}^{\left(-x+2\right)}}$
Equate the exponents: $2\left(x-1\right)=3\left(-x+2\right)$
Solve for x:
$2x-2=-3x+8$
$2x=-3x+8$
$5x=8$
$x=\frac{8}{5}$ or 1.6

Jeffrey Jordon