Question

Resolva as equações exponenciais:


a)4^x = √32
b)5(elevado na 3x-3) -4 = 121
c)9^x + 3^x = 90

Answer 1

$4^{x}=32^{1/2}\\\\(2^{2})^{x}=(2^{5})^{1/2}\\\\2x=5\cdot 1/2\\\\\dfrac{2x}{1/2}=5\\\\4x=5\\\\\boxed{x=5/4}$

$5^{3x-3}=121+4\\\\5^{3x-3}=125\\\\5^{3x-3}=5^{3}\\\\3x-3=3\\\\3x=3+3\\\\x=6/3\\\\\boxed{x=2}$

$(3^{2})^{x}+3^{x}=3^{4}+3^{2}\\\\2x+x=4+2\\\\3x=6\\\\x=6/3\\\\\boxed{x=2}$