Is it possible to transform this equation?

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However, if you take the natural logarithm of both sides, you can use the logarithm rule that ln(ab) = ln(a) + ln(b) to show that the left expression is equivalent to the right expression. Therefore, the answer is yes, it is possible to transform the equation in this way. In summary, it is possible to transform the given equation using the logarithm rule for product to obtain the desired expression.
  • #1
somasimple
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Hi,

Is it possible to transform this equation
$$ln⁡((p_1 C_1)/(p_1 C_2 ))+ln⁡((p_2 C_3)/(p_2 C_4 ))+ln⁡((p_3 C_5)/(p_3 C_6 ))$$
to
$$ln⁡((p_1 C_1+p_2 C_3+p_3 C_5)/(p_1 C_2+p_2 C_4+p_3 C_6 ))$$
Thanks
 
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  • #2
Have you tried testing it with real values to see if its true?

##ln(1/2) + ln(3/4) + ln(5/6) =?= ln ( (1 + 3 + 5)/(2 + 4 + 6) )##

##ln(1/2) + ln(3/4) + ln(5/6) = -1.16315080981 ##

##ln ( (1 + 3 + 5)/(2 + 4 + 6) ) = -0.28768207245 ##

Did I do the test right?

I used the subscripts for the C values as their values and used Google to compute the results. If the two expressions were equivalent then the results should match too.
 
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  • #3
somasimple said:
Hi,

Is it possible to transform this equation
$$ln⁡((p_1 C_1)/(p_1 C_2 ))+ln⁡((p_2 C_3)/(p_2 C_4 ))+ln⁡((p_3 C_5)/(p_3 C_6 ))$$
to
$$ln⁡((p_1 C_1+p_2 C_3+p_3 C_5)/(p_1 C_2+p_2 C_4+p_3 C_6 ))$$
Thanks
And just a small point -- each of the lines you wrote above is an expression, not an equation. An equation will have an equal sign in it. :smile:

https://en.wikipedia.org/wiki/Expression_(mathematics)
 
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  • #4
Hi,
Thanks for the answer and clarification.
i took the right member of the equation and omitted the left part ;-)
I found the same results as you but wanted some insurance.
 
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  • #5
somasimple said:
Hi,

Is it possible to transform this equation
$$ln⁡((p_1 C_1)/(p_1 C_2 ))+ln⁡((p_2 C_3)/(p_2 C_4 ))+ln⁡((p_3 C_5)/(p_3 C_6 ))$$
to
$$ln⁡((p_1 C_1+p_2 C_3+p_3 C_5)/(p_1 C_2+p_2 C_4+p_3 C_6 ))$$
Thanks

You are effectively asking if [tex]
\frac{p_1C_1}{p_1C_2} \frac{p_2 C_3}{p_2 C_4} \frac{p_3 C_5}{p_3 C_6} =
\frac{p_1 C_1 + p_2 C_3 + p_3 C_5}{p_1 C_2 + p_2 C_4 + p_3 C_6}.[/tex] This is not true in general.
 
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Related to Is it possible to transform this equation?

1. Can any equation be transformed into a different form?

Yes, any equation can be transformed into a different form as long as the rules of algebra are followed.

2. What methods can be used to transform an equation?

There are several methods that can be used to transform an equation, including substitution, elimination, and graphing.

3. Can an equation be transformed without changing its solutions?

Yes, an equation can be transformed without changing its solutions as long as the transformations are done using equivalent operations.

4. Are there any limitations to transforming an equation?

There are some limitations to transforming an equation, such as not being able to divide by zero or taking the square root of a negative number.

5. How can transforming an equation be useful in scientific research?

Transforming an equation can be useful in scientific research because it allows for simplification and manipulation of equations to better understand relationships between variables and make predictions.

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