First I've written $\log_{12} 18=a$ in terms of base 24 and then did the same to $\log_{24} 54=b$ and written it in terms of base 12. That gave me a value of $a=\frac{\log_{24} 2+2\log_{24} 3} {2\log_{24} 2+\log_{24} 3}$
I did the same thing with $b$ and put the values of $a$ and $b$ in $ab+5(a-b)=1$
now how do I find the common denominator and simplify the equation and prove it?