B Is it possible to transform this equation?

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somasimple

Gold Member
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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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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.
 

berkeman

Mentor
55,087
5,316
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:

 

somasimple

Gold Member
742
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.
 

pasmith

Homework Helper
1,717
395
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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