Question

ajudem com algumas exponenciais 

64.2^x -1=0
3^x-1 -3^x+1 =-8
(1/100)^2x =0,0001

Answer 1

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a)
$64.2^x-1=0 \\ 64.2^x=1 \\ 2^x= \frac{1}{64}$

$2^x=64^-^1 \\ 2^x=(2^6)^-^1 \\ 2^x=2^{-6} \\ x=-6$

S={-6 }

b)
$3^{x-1}-3^{x+1}=-8$

$3^x.3^{-1}-3^x.3=-8 \\ 3^x(3^{-1}-3)=-8$

$3^x( \frac{1}{3} -3)=-8$

$3^x( \frac{1-9}{3})=-8$

$3^x(- \frac{8}{3} )=-8$

$3^x=-8:(- \frac{8}{3} )$

$3^x=-8.(- \frac{3}{8})$

$3^x=-(-3) \\ 3^x=3 \\ x=1$

S={1}

c)
$( \frac{1}{100} )^{2x}=0,0001 \\ (100^{-1})^{2x}=10^{-4} \\ (10^{-2})^{2x}=10^}^{-4 } \\ -2(2x)=-4 \\ -4x=-4 \\ 4x=4 \\ x=1$

S={ 1 }