How do I manipulate this to the form desired?

[shreddinglicks]

Homework Statement

I want to manipulate an equation to suit a desired form.

Homework Equations

$(-h^2/2uc)*(dp/dx)*ln((1+c*(x/h)^2)/(1+c))$

becomes

$-(h^2/2u)*(dp/dx)*(1-(x/h)^2)$

The Attempt at a Solution

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

 

[Dick]

Homework Statement

I want to manipulate an equation to suit a desired form.

Homework Equations

$(-h^2/2uc)*(dp/dx)*ln((1+c*(x/h)^2)/(1+c))$

becomes

$-(h^2/2u)*(dp/dx)*(1-(x/h)^2)$

The Attempt at a Solution

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

They are using the approximation $\ln(1+a) \approx a$ valid when $a$ is small. Try that along with other rules about logs.

 

[shreddinglicks]

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]

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.

 

[shreddinglicks]

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.