[tex] \log_{2}5 = a,\quad \log_{2}3=b \\ \\ \log_{15}12 = \dfrac{\log_{2}12}{\log_{2}15} = \dfrac{\log_2{(3\cdot 4)}}{\log_{2}(3\cdot 5)} = \dfrac{\log_{2}3+ \log_{2}4}{\log_{2}3 +\log_{2}5} \Rightarrow \\ \\ \Rightarrow \log_{12}15 = \dfrac{b+2}{b+a} \Rightarrow \boxed{\log_{12}15 = \dfrac{2+b}{a+b}} [/tex]
