Can Ln and Logarithmic Expressions Be Further Simplified?

In summary, we are discussing the expression Ln(log7-log76)=Ln(log77) and how to simplify it. It is pointed out that there appears to be a mistake in the expression, as the antilog is missing in one of the "log" expressions. Then, the idea of adding or subtracting logarithms of the same base is suggested as a way to simplify the expression. It is also noted that log(A) + log(B) = ? and log(A) - log(B) = ? can be helpful in this case. Finally, it is concluded that if the expression is indeed log7 7, then it can be simplified to just ln(1)= 0.
  • #1
skelitor413
1
0
is it possible to simplify this more??

Ln(log7-log76)=

Ln(log77)
 
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  • #2
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)=
 
  • #3
... to continue, search in your book about adding or subtracting logarithms of the same base. log(A) + log(B) = ? and log(A) - log(B) = ?
 
  • #4
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?
 

Related to Can Ln and Logarithmic Expressions Be Further Simplified?

1. What is the difference between LN and logs?

LN stands for natural logarithm and is represented by the base e, while logs refer to logarithms with a base other than e. LN is a specific type of logarithm, while logs can have a variety of bases.

2. How do I simplify LN and logs?

To simplify LN and logs, you can use logarithmic rules such as the product rule, quotient rule, power rule, and change of base rule. These rules allow you to simplify expressions involving LN and logs to a single number or variable.

3. Is it possible to simplify complex expressions involving LN and logs?

Yes, it is possible to simplify complex expressions involving LN and logs by using the logarithmic rules and properties. It may require some algebraic manipulation and simplification, but it is achievable with practice.

4. Can LN and logs be used to solve equations?

Yes, LN and logs can be used to solve equations involving exponential and logarithmic functions. By applying the inverse properties of LN and logs, you can isolate the variable and solve for its value.

5. What are the common applications of LN and logs in science?

LN and logs are commonly used in scientific fields such as biology, chemistry, and physics to model exponential growth and decay, measure sound intensity and earthquakes, and study population dynamics. They are also used in finance and economics to calculate interest rates and compound growth.

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