Can Ln and Logarithmic Expressions Be Further Simplified?

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Discussion Overview

The discussion centers around the simplification of logarithmic expressions, specifically the expression Ln(log7 - log76) and its potential equivalence to Ln(log77). Participants explore whether further simplification is possible and discuss the properties of logarithms.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the correctness of the expression, suggesting that an antilog may be missing in the logarithmic terms.
  • Another participant prompts others to recall the properties of logarithms, specifically how to add or subtract logarithms of the same base.
  • A different participant proposes that the expression could be interpreted as ln(log7(x) - log7(6)), leading to the conclusion that log7(x/6) could simplify to log7(7) if x equals 42.
  • This same participant concludes that since log7(7) equals 1, the expression simplifies to ln(1), which equals 0.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the original expression and its simplification. Some participants challenge the initial formulation, while others provide alternative interpretations and simplifications. The discussion remains unresolved regarding the correctness of the initial expression and the implications of the proposed simplifications.

Contextual Notes

There are missing assumptions regarding the variables involved in the logarithmic expressions, particularly the unspecified value of x. The discussion also depends on the definitions and properties of logarithms, which may not be universally agreed upon by all participants.

skelitor413
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is it possible to simplify this more??

Ln(log7-log76)=

Ln(log77)
 
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skelitor413 said:
is it possible to simplify this more??

Ln(log7-log76)=

Ln(log77)

To start with, some of that does not look correct. You are missing the antilog in one of your "log" expressions. (log7(ofWhat?)-log76)=
 
... to continue, search in your book about adding or subtracting logarithms of the same base. log(A) + log(B) = ? and log(A) - log(B) = ?
 
skelitor413 said:
is it possible to simplify this more??

Ln(log7-log76)=

Ln(log77)
Persumably you mean ln(log7 x- log7 6) for some number x that you forgot. Certainly log7 x- log7 6= log7(x/6). If that is, as you appear to be saying, log7 7, then x must have been equal to 7(6)= 42.
Yes, ln(log7(42)- log7(6))= ln(log7 7)

Further, by the very definition of log, log7= 1 so what you have reduces to just ln(1)= 0. It that simple enough?
 

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