High School Is it possible to transform this equation?

[somasimple]

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

 

[jedishrfu]

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]

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.

https://en.wikipedia.org/wiki/Expression_(mathematics)

 

[somasimple]

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]

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 <br /> \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} =<br /> \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}. This is not true in general.