Express logarithm in another variable

[songoku]

Homework Statement

Given that $\log_{6} 30=m$ and $\log_{6} 20=n$, express $\log_{6} 3$ in $m$ or $n$

Relevant Equations

logarithm property

The best I can get is:

$$\log_{6} 3=m-n+\log_{6} 2$$

Is it possible to get the final answer in terms of $m$ and $n$ only? If yes, I will try to do it again

Thanks

 

[anuttarasammyak]

You can make use of the below
$$\log_63=1-\log_62$$
$$\log_65+1=m$$
$$2\log_62+\log_65=n$$

 

[Delta2]

what you did is correct. you need to complete it by using $\log_6(2\cdot3)=1$, so that you will have two equations with two unknowns (unknowns can be considered to be the $\log_6 2$ and $\log_6 3$.)

 

[vela]

Try adding $\log_6 3$ to both sides.

 

[songoku]

Thank you very much anuttarasammyak, Delta2, vela