![1) \: log_{10}( \sqrt[6]{10} ) = \frac{1}{6} log_{10}(10) = \frac{1}{6} \\ log_{2}( \sqrt{2} ) = \frac{1}{2} log_{2}(2) = \frac{1}{2}](https://tex.z-dn.net/?f=1%29+%5C%3A+log_%7B10%7D%28+%5Csqrt%5B6%5D%7B10%7D+%29+%3D+%5Cfrac%7B1%7D%7B6%7D+log_%7B10%7D%2810%29+%3D+%5Cfrac%7B1%7D%7B6%7D+%5C%5C+log_%7B2%7D%28+%5Csqrt%7B2%7D+%29+%3D+%5Cfrac%7B1%7D%7B2%7D+log_%7B2%7D%282%29+%3D+%5Cfrac%7B1%7D%7B2%7D+ "1) \: log_{10}( \sqrt[6]{10} ) = \frac{1}{6} log_{10}(10) = \frac{1}{6} \\ log_{2}( \sqrt{2} ) = \frac{1}{2} log_{2}(2) = \frac{1}{2}")
т. к. 1/6<1/2, то <br>
![log_{10}( \sqrt[6]{10} ) < log_{2}( \sqrt{2} )](https://tex.z-dn.net/?f=+log_%7B10%7D%28+%5Csqrt%5B6%5D%7B10%7D+%29+%3C+log_%7B2%7D%28+%5Csqrt%7B2%7D+%29+ "log_{10}( \sqrt[6]{10} ) < log_{2}( \sqrt{2} )")
3) log_5(1/625)=log_5(1/5^4)=log_5(5^(-4))=-4log_5(5)=-4
log_3(1/27)=log_3(1/3^3)=log_3(3^(-3))=-3log_3(3)=-3
т. к. -4<-3, то log_5(1/625)<log_3(1/27)<br>
2) log_4(2)=log_(2^2)(2)=1/2*log_2(2)=1/2
log_0,0625(0,25)=log_(0,25^2)(0,25)=1/2*log_0,25(0,25)=1/2
т. к. 1/2=1/2, то log_4(2)=log_0,0625(0,25)
4) log_10(2)=(log_4(2))/(log_4(10))=(log_2^2(2))/(log_4(10))=1/2*log_2(2)/(log_4(10))=1/(2*log_4(10))
1/log_4(1000)=1/log_4(10^3)=1/(3*log_4(10))
т. е. 2<3, то log_10(2)>1/log_4(1000)