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How do I manipulate this to the form desired?

1. The problem statement, all variables and given/known data
I want to manipulate an equation to suit a desired form.

2. Relevant equations
##(-h^2/2uc)*(dp/dx)*ln((1+c*(x/h)^2)/(1+c))##

becomes

##-(h^2/2u)*(dp/dx)*(1-(x/h)^2)##
3. The attempt at a solution

I have no idea, I'm not even sure how the natural log disappears.
 

Dick

Science Advisor
Homework Helper
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615
1. The problem statement, all variables and given/known data
I want to manipulate an equation to suit a desired form.

2. Relevant equations
##(-h^2/2uc)*(dp/dx)*ln((1+c*(x/h)^2)/(1+c))##

becomes

##-(h^2/2u)*(dp/dx)*(1-(x/h)^2)##
3. The attempt at a solution

I have no idea, I'm not even sure how the natural log disappears.
They are using the approximation ##\ln(1+a) \approx a## valid when ##a## is small. Try that along with other rules about logs.
 
They are using the approximation ##\ln(1+a) \approx a## valid when ##a## is small. Try that along with other rules about logs.
I see:

Use ##ln(x/y) = ln(x) - ln(y)##

The rest is simple.

Is there a link to somewhere online showing that approximation you gave? Just curious.
 

Dick

Science Advisor
Homework Helper
26,252
615
Is there a link to somewhere online showing that approximation you gave? Just curious.
I don't know any good links. But approximations like this generally come from taking the first terms of the Taylor series. ##\ln(1+x)=x-
\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots## Keeping just the first term gives the approximation. Similarly, ##\sin(x) \approx x## etc.
 
I don't know any good links. But approximations like this generally come from taking the first terms of the Taylor series. ##\ln(1+x)=x-
\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots## Keeping just the first term gives the approximation. Similarly, ##\sin(x) \approx x## etc.
Thanks.
 

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