Question

Funções exponenciais, preciso pra hj obrigado !!

Answer 1

j)
$10. 2^{ x^{2} -4} =320 \\ 2^{ x^{2} -4} =320\div10 \\ 2^{ x^{2} -4} =32 \\ 2^{ x^{2} -4} =2^5$

$x^{2} -4=5 \\ x^{2} =5+4 \\ x^{2} =9 \\ x=\pm \sqrt{9 } \\ x=\pm3$


a)
$10^{ x^{2} -2x-2} =10$

$x^{2} -2x-2-1=0 \\ x^{2} -2x-3=0$

Δ=b²-4ac
Δ=4+12
Δ=16
√Δ=√16

$x= \frac{-(-2)\pm \sqrt{16} }{2} = \frac{2\pm4}{2}$

$x'= \frac{2+4}{2} = \frac{6}{2}=3$

$x"= \frac{2-4}{2} =- \frac{2}{2} =-1$

S={-1,3}