# 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

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

Last edited:
songoku
Homework Helper
Gold Member
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##.)

songoku
Staff Emeritus