Proof the expession ${\mathrm{log}}_{12}18\times {\mathrm{log}}_{24}54+5({\mathrm{log}}_{12}18-{\mathrm{log}}_{24}54)=1$

I am trying to proof the following expression (without a calculator of course).

${\mathrm{log}}_{12}18\times {\mathrm{log}}_{24}54+5({\mathrm{log}}_{12}18-{\mathrm{log}}_{24}54)=1$

I know this isn't a difficult task but it's just killing me. I have tried many things, among which was base transformation to 12 and expressing every logarithm in terms of ${\mathrm{log}}_{12}3$ and ${\mathrm{log}}_{12}2$ but every time I try to do it, I mess up something. I don't know if my concentration is terrible or I'm doing something wrong.

Thanks ;) ( if there are more levels to this task, I'd like a hint, not a complete solution)

I am trying to proof the following expression (without a calculator of course).

${\mathrm{log}}_{12}18\times {\mathrm{log}}_{24}54+5({\mathrm{log}}_{12}18-{\mathrm{log}}_{24}54)=1$

I know this isn't a difficult task but it's just killing me. I have tried many things, among which was base transformation to 12 and expressing every logarithm in terms of ${\mathrm{log}}_{12}3$ and ${\mathrm{log}}_{12}2$ but every time I try to do it, I mess up something. I don't know if my concentration is terrible or I'm doing something wrong.

Thanks ;) ( if there are more levels to this task, I'd like a hint, not a complete solution)