Question

resolva, em IR:

a) 4 elevado a x = (½) elevado a x elevado a 2 - elevado a x


b) 25 elevado a x = (1/125) elevado a x - 3

Answer 1

vamos lá...

a)
$4^x=( \frac{1}{2} )^{x^2-x} \\ \\ 2^{2x=(2^{-1})^{x^2-x}}\\ \\ \not2^{2x}=\not2^{-x^2+x} \\ \\ 2x=-x^2+x \\ \\ x^2+2x-x=0 \\ \\ x^2+x=0 \\ \\ \\ x(x+1)=0 \\ \\ x+1=0~~~~e~~~~x=0 \\ x=-1 \\ \\ S=\{-1,0\}$ 

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b)
$25^x=( \frac{1}{125} )^{x-3} \\ \\ 5^{2x}=(5^{-3})^{x-3} \\ \\\not5^{2x}=\not5^{-3x+9} \\ \\ 2x=-3x+9 \\ \\ 2x+3x=9 \\ \\ 5x=9 \\ \\ x= \frac{9}{5}$