Свойства логарифма Вычислите:

1) log₆108*12-log₆6=log₆6⁴-1=4-1=3;

2) log₂(1/√2)-log₂(1/√2)=log₂(1/√2:1/√2)=log₂1=0;

3) $\frac{(log_510-log_52)(log_510+log_52)}{log_320}=log_55log_520:\frac{log_520}{log_53}=log_53$

4) $4^{0,5}*4^{-log_25}-log_3(\frac{1}{3}*log_55)=2*(\frac{1}{2^{log_25}})^2-log_33^{-1}=2*(\frac{1}{5})^2+log_33=\frac{2}{25}+1=1\frac{2}{25}$

5) $lg5*(lg10+lg2)+lg^22=lg5*(1+lg2)+lg^22=lg5+lg2*lg5+lg^22=lg5+lg2(lg5+lg2)=lg5+lg2(lg10)=lg5+lg2=lg10=1$

6) $log_{5^{0,5}}2^2log_{7^2}5*log_{2^3}7=\frac{2}{0,5*2*3}log_52log_75*log_27=\frac{2}{3}\frac{lg2}{lg5}\frac{lg5}{lg7}\frac{lg7}{lg2}=\frac{2}{3}$