Trying to simplify the derivative of this to find a constant,

y = ln[{lnx/A}/{1-[lnx/A]}]

The best I can is get to

y'=ln[lnx/{A-lnx}]

Any ideas?

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- Apr 8th 2008, 04:46 PMtheowneSimplifying natural logarithm
Trying to simplify the derivative of this to find a constant,

y = ln[{lnx/A}/{1-[lnx/A]}]

The best I can is get to

y'=ln[lnx/{A-lnx}]

Any ideas? - Apr 8th 2008, 04:54 PMMathstud28Ok here is what you do
$\displaystyle \ln\bigg[\frac{\frac{\ln(x)}{A}}{1-\frac{\ln(x)}{A}}\bigg]$...and using the rules you can get it to $\displaystyle ln\bigg[\frac{\ln(x)}{A}\bigg]-\ln\bigg[1-\frac{\ln(x)}{A}\bigg]$...so you can then go $\displaystyle ln(ln(x))-ln(A)-ln\bigg[\frac{1}{A}\bigg[A-\ln(x)\bigg]\bigg]$

which goes to $\displaystyle ln(ln(x))-ln(A)+ln(A)+ln[A-ln(x)]$...$\displaystyle ln(ln(x))-ln[A-ln(x)]$