a)
log_{12}2+log_{12}8+log_{12}9=log_{12}(2*8*9)=log_{12}144=log_{12}12^2=2
b)
log_3\frac{1}{12}+log_3\frac{14}{15}+log_3\frac{10}{21}=log_3(\frac{1}{12}*\frac{\not14^2}{\not15^3}*\frac{\not10^2}{\not21^3})=log_3\frac{4}{108}=log_3\frac{1}{27}=
=log_327^{-1}=log_3(3^3)^{-1}=log_33^{-3}=-3
c)
log0,12-log0,3+log25=log(\frac{0,12}{0,3}*25)=log(\frac{12}{30}*25)=log(\frac{2}{\not5^1}*\not25^5)=
=log_{10}10=1
d)
log_{0,2}0,3-log_{0,2}0,5-log_{0,2}15=log_{0,2}(\frac{3}{10}:\frac{5}{10}:15)=
=log_{\frac{2}{10}}(\frac{\not3^1}{\not10^1}*\frac{\not10^1}{5}*\frac{1}{\not15^5})=log_{\frac{1}{5}}\frac{1}{25}=log_{\frac{1}{5}}(\frac{1}{5})^2=2