Chapter 8.1B, Problem 19A

In each of the following, find all real numbers x that satisfy the given equation. If none satisfy the equation, then state the answer as "None."

a. $3^x{=}^{-}243$

b. ${81}^{-x}=27$

c. ${\left(\frac{4}{9}\right)}^{-3x}=\frac{32}{243}$

d. $\sqrt[3]{{}^{-}x}=2\sqrt[3]{3}$

e. $x^{-\frac{2}{5}}=2$

f. ${\left(x+1\right)}^2=2$