Question

me ajudem por favor eh pra amanha...
calcule a funçao y=log na base 1/2 e no logaritimando x
os valores de x eh:
1/8
1/4
1/2
1
2
3
4

Answer 1

$a) log_{ \frac{1}{2}}\frac{1}{8}=y \\ \frac{1}{8}=(\frac{1}{2})^{y}\\ \frac{1}{2^{3}}= 2^{-y} \\ 2^{-y}= 2^{-3} \\ -y=-3 \\ y=3 \\ b) log_{\frac{1}{2}} \frac{1}{4}=y\\ \frac{1}{4}= (\frac{1}{2})^{y} \\ 2^{-2}= 2^{-y} \\ -y=-2 \\ y=2 \\ c) log_{ \frac{1}{2}}\frac{1}{2}=y \\ ( \frac{1}{2})^{1}= (\frac{1}{2})^{y } \\ y=1 \\ d) log_{\frac{1}{2}}1=y \\ 1= (\frac{1}{2}^{y} \\ (\frac{1}{2})^{y}=(\frac{1}{2}^{0} \\ y=0 \\ e) log_{ \frac{1}{2}}2=y \\ 2^{-y}= 2^{1} \\ -y=1 \\ y=-1$