Express logarithm in another variable

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.
  • #1
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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
 
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  • #2
You can make use of the below
[tex]\log_63=1-\log_62[/tex]
[tex]\log_65+1=m[/tex]
[tex]2\log_62+\log_65=n[/tex]
 
Last edited:
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  • #3
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##.)
 
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  • #4
Try adding ##\log_6 3## to both sides.
 
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  • #5
Thank you very much anuttarasammyak, Delta2, vela
 

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