Hi guys

I can't solve the following exponential equation:

n * 11^n = 132

Any help will be appreciated!

Thanks in advance,

Matan

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- Oct 7th 2010, 03:05 PMmatancs92Exponential equation
Hi guys

I can't solve the following exponential equation:

n * 11^n = 132

Any help will be appreciated!

Thanks in advance,

Matan - Oct 7th 2010, 05:36 PMskeeter
- Oct 7th 2010, 07:00 PMEducated

You cannot solve this normally, or get the exact result of it. You can only get an approximation of it (down to however many decimal places you want.)

A method that can be used to solve this is the Newton–Raphson method.

Rearrange the formula to make one side equal zero, and call this f(x).

Select an appropriate number to start off with, call this and apply the newton method. - Oct 8th 2010, 04:24 AMHallsofIvy
You can give an "algebraic" solution in terms of the Lambert W function, W(x), which is

**defined**as the inverse function to .

Of course, . If we let , then and the equation becomes .

Then so and . - Oct 9th 2010, 05:47 AMmatancs92
Thank you very much for helping me guys! :)