Question

Por Favor, como resolver esses exercícios..

Answer 1

a)
$log 0,5^{x+1} = 4 \\ \\ log ( \frac{1}{2})^{2} = 2^{2} \\ (2^{-1})^{x+1} = 2^{2} \\ -x-1 = 2 \\ -x = 2+1 \\ -x = 3 \\ x = -3$

b)
$log 10^{2x}=25 \\ log 100^{x} = 25 \\ x*log100 = 25 \\ x*10 = 25 \\ x = 25/10 \\ x = 2,5$

c)
$log_{x+5}(4x+7) = 10^{0} \\ \\ log_{x+5}(4x+7) = 1 \\ (x+5)^{1} = 4x+7 \\ x+5 = 4x+7 \\ x-4x = 7-5 \\ -3x = 2 \\ x=- \frac{2}{3}$

d)
$log_4( x^{2} +7) = 2 \\ \\ x^{2} +7 = 4^{2} \\ x^{2} +7 = 16 \\ x^{2} =16-7 \\ x^{2} =9 \\ x=+-3$

x' =-3
x'' =3