# Express logarithm in another variable

• songoku
In summary, an express logarithm in another variable is a mathematical expression that represents the logarithm of a given number in terms of another variable. This can be done using the change of base formula, which allows for easier manipulation and calculation of logarithms. Expressing a logarithm in another variable also has benefits such as simplifying equations, facilitating comparison and analysis of different functions, and generalizing rules and properties. Some examples of expressing a logarithm in another variable include rewriting log<sub>3</sub> 27 as log<sub>3</sub> x and expressing ln 8 as ln x.

#### 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

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
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
Try adding ##\log_6 3## to both sides.

songoku
Thank you very much anuttarasammyak, Delta2, vela