a)
[tex]\it log_{12}5\cdot log_{11}7=\dfrac{log_{11} 5}{log_{11}12}\cdot\dfrac{log_{12}7}{log_{12}11}=\dfrac{log_{11}5\cdot log_{12}7}{log_{11}12\cdot\dfrac{1}{log_{11}12}}=log_{11}5\cdot log_{12}7[/tex]
b)
[tex]\it log_a b\cdot log_b c\cdot log_c a=log_a b\cdot\dfrac{log_a c}{log_a b}\cdot\dfrac{log_a a}{log_a c}=log_a a=1[/tex]
