Zadanie 1 i Zadanie 2 link do Rozwiązania
Zadanie 3
a)
x=log_232=log_22^5=5
y=log10^6=6
y>x
b)
x=log0,01=log(\frac{1}{100})=log100^{-1}=log(10^2)^{-1}=log10^{-2}=-2
y=log_2\frac{1}{8}=log_2(\frac{1}{2})^3=log_22^{-3}=-3
x>y
c)
x=log_82=log_8\sqrt[3]{8}=log_88^{\frac{1}{3}}=\frac{1}{3}
y=log\sqrt{10}=log10^{\frac{1}{2}}=\frac{1}{2}
y>x
d)
x=log(log10)=log1=log10^0=0
y=log_{\frac{1}{2}}2=log_{\frac{1}{2}}(\frac{1}{2})^{-1}=-1
x>y
e)
x=log_4(log_216)=log_4(log_22^4)=log_44=1
y=log10\sqrt{10}=log10^1*10^{\frac{1}{2}}=log10^{1\frac{1}{2}}=1\frac{1}{2}
y>x
f)
x=log_{\frac{1}{4}}(log100)=log_{\frac{1}{4}}(log10^2)=log_{\frac{1}{4}}2=log_{\frac{1}{4}}\sqrt4=log_{\frac{1}{4}}4^{\frac{1}{2}}=
=log_{\frac{1}{4}}(\frac{1}{4})^{-\frac{1}{2}}=-\frac{1}{2}
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y=log_{\sqrt2}2=log_{\sqrt2}(\sqrt2)^2=2
y>x