Question

So sánh :

a. \(\sqrt[4]{\sqrt{3}-1}\) và \(\sqrt[3]{\sqrt{3}-1}\)

b. \(\log_32\) và \(\log_23\)

 

Answer 1

a. \(\sqrt[4]{\sqrt{3}-1}\) và \(\sqrt[3]{\sqrt{3}-1}\)

Ta có : \(\begin{cases}\sqrt[4]{\sqrt{3}-1}=\left(\sqrt{3}-1\right)^{\frac{1}{4}};\sqrt[3]{\sqrt{3}-1}=\left(\sqrt{3}-1\right)^{\frac{1}{3}}\\0< \sqrt{3}-1< 1;\frac{1}{4}< \frac{1}{3}\end{cases}\)

             \(\Rightarrow\sqrt[4]{\sqrt{3}-1}>\left(\sqrt{3}-1\right)^{\frac{1}{4}}\)

 

b. \(\log_32\) và \(\log_23\)

Ta có : \(\log_32< \log_33=1=\log_22< \log_23\Rightarrow\log_32< \log_23\)