# Simplifying natural logarithm

• April 8th 2008, 05:46 PM
theowne
Simplifying 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?
• April 8th 2008, 05:54 PM
Mathstud28
Ok here is what you do
Quote:

Originally Posted by theowne
Trying to simplify this to get a constant rather than a variable...

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

The best I can is get to

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

Any ideas?

$\ln\bigg[\frac{\frac{\ln(x)}{A}}{1-\frac{\ln(x)}{A}}\bigg]$...and using the rules you can get it to $ln\bigg[\frac{\ln(x)}{A}\bigg]-\ln\bigg[1-\frac{\ln(x)}{A}\bigg]$...so you can then go $ln(ln(x))-ln(A)-ln\bigg[\frac{1}{A}\bigg[A-\ln(x)\bigg]\bigg]$
which goes to $ln(ln(x))-ln(A)+ln(A)+ln[A-ln(x)]$... $ln(ln(x))-ln[A-ln(x)]$