Ayaana Buck

2021-02-08

diskusje5

Skilled2021-02-09Added 82 answers

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: ${\left({a}^{m}\right)}^{n}={a}^{m}n$ ${3}^{2}(x-1)={3}^{{2}^{(-x+2)}}$

Equate the exponents: $2(x-1)=3(-x+2)$

Solve for x:

$2x-2=-3x+8$

$2x=-3x+8$

$5x=8$

$x=\frac{8}{5}$ or 1.6

Jeffrey Jordon

Expert2021-08-10Added 2575 answers

Video solution for you