Logarithm Verification: Proving logbx = logax/logab for a, b > 0

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Homework Help Overview

The discussion revolves around verifying the logarithmic identity logbx = logax/logab for positive values of a and b. Participants are exploring the properties of logarithms and their relationships.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express 'x' in terms of 'z' and 'b' by defining z as logbx. There is a question about the next steps after establishing this relationship.

Discussion Status

The discussion is active, with participants engaging in reasoning about logarithmic properties. Some guidance has been offered regarding taking logarithms of both sides of an equation, indicating a potential direction for further exploration.

Contextual Notes

There appears to be uncertainty regarding the initial steps to take in verifying the logarithmic identity, as well as the implications of the definitions being used.

magnifik
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Homework Statement


Verify the formula logbx = logax/logab for a, b > 0


Homework Equations





The Attempt at a Solution


I don't even know how I would go about starting this...
 
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magnifik said:

The Attempt at a Solution


I don't even know how I would go about starting this...

If we let z=logbx, then what is 'x' equal to in terms of 'z' and 'b'?
 
rock.freak667 said:
If we let z=logbx, then what is 'x' equal to in terms of 'z' and 'b'?

x=bz
?
 
magnifik said:
x=bz
?

and if you take the loga of both sides of the equation, what does it reduce to?
 
omg thanks so much! lol that was a lot easier than i thought it would be
 

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