Question

Resolva as seguintes equações exponenciais:

* 2.(1/4)^2x-3 = 4

*(0,2)^x-2 = 1

*(1/3)^ -4+x = 9^x+3

Answer 1

$2.( \frac{1}{4}) ^{2x-3}=4\\\\ ( \frac{1}{2}) ^{2x-3}=2 ^{2}\\\\ (2 ^{-1}) ^{2x-3}=2 ^{2}\\\\ \not2 ^{-2x+3}=\not2 ^{2}\\\\ -2x+3=2\\ -2x=2-3\\ -2x=-1\\ x=(-1)/(-2)\\ x=1/2\\\\ \boxed{S=\{ \frac{1}{2}\}}$

_______________

$(0,2) ^{x-2}=1\\ (0,2) ^{x-2}=(0,2) ^{0}\\ x-2=0\\ x=2\\\\ \boxed{S=\{2\}}$

_______________

$( \frac{1}{3}) ^{-4+x}=9 ^{x+3}\\\\ (3 ^{-1}) ^{-4+x}=(3 ^{2}) ^{x+3} \\\\ \not3 ^{4-x}=\not3 ^{2x+6}\\\\ 4-x=2x+6\\ -x-2x=6-4\\ -3x=2\\ x=2/(-3)\\ x=-2/3\\\\ \boxed{S=\{- \frac{2}{3}\}}$


Espero ter ajudado e tenha ótimos estudos :)