Question

Resolva as equacoes ecponenciais:
a) 100^(x+3)= 1/10
b) 9^(x-2)=√27

Answer 1

a)

$100^{x+3}=\frac{1}{10}\\ \\ 10^{10(x+3)}=10^{-1}\\ \\ 10(x+3)=-1\\ \\ x+3=\frac{-1}{10}\\ \\ x=-3-\frac{1}{10}\\ \\ x=-\frac{31}{10}$

b)

$9^{x+2}= \sqrt{27}\\ \\ 3^{2(x+2)}= \sqrt{3^3}\\ \\ 3^{2x+4}=3^{\frac{3}{2}}\\ \\ 2x+4=\frac{3}{2}\\ \\ 4x+8=3\\ \\ 4x=3-8\\ \\ 4x=-5\\ \\ x=-\frac{5}{4}$

Answer 2

$100^{(x+3)} = \frac{1}{10}$

$( 10^{2}) ^{x+3}= 10^{-1}$

$2x+6=-1-->2x=-7-->x=- \frac{7}{2}$

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$9^{(x-2)} = \sqrt{27} =$

$( 3^{2})^(^x^-^2^)= \sqrt{3^3}$

$3^(^2^x^-^4^)= 3^{ \frac{3}{2} }$

$2x-4= \frac{3}{2} -->2x= \frac{3}{2} +4$

$2x = \frac{11}{2}-->x= \frac{11}{2} . \frac{1}{2} -->x= \frac{11}{4}$