# Solving a weird logarithmic equation

• Apr 6th 2011, 10:00 AM
ohms
Solving a weird logarithmic equation
This is really part of a Dynamics problem, but I'm running into a purely algebraic problem:

$12 = -(1/k)*ln(1-6k)$

How on earth do you manually solve for k?? Nothing I learned in pre-uni would be able to solve this. Solutions tell you to 'guess and check' ... (Headbang)
• Apr 6th 2011, 10:02 AM
Ackbeet
You'd have to use the ProductLog function, or Lambert's W function, as it's also called. Here's the solution for you.
• Apr 6th 2011, 03:07 PM
CaptainBlack
Quote:

Originally Posted by ohms
This is really part of a Dynamics problem, but I'm running into a purely algebraic problem:

$12 = -(1/k)*ln(1-6k)$

How on earth do you manually solve for k?? Nothing I learned in pre-uni would be able to solve this. Solutions tell you to 'guess and check' ... (Headbang)

For a numerical solution you would normally use Newton-Raphson.

CB