I can't solve the equation (for variable ): .

Help!

Thanks!

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- August 5th 2010, 03:20 AMRieszExponential equation
I can't solve the equation (for variable ): .

Help!

Thanks! - August 5th 2010, 03:35 AMsa-ri-ga-ma
Can you explain the symbols in the equation?

- August 5th 2010, 04:04 AMRiesz
Sure, sorry!

is the unknown variable, and are known positive constant. - August 5th 2010, 04:07 AMHallsofIvy
That cannot be solved in terms of elementary functions. You can do this:

Let u= T+ E. Then E= u- T so and

The equation is now or .

Now, let v= u/T so that u= TV. The equation becomes or .

Now you can use "Lambert's W function" which is defined as the inverse to the function

Then .

Then, of course, and . - August 5th 2010, 09:29 AMRiesz
Let .

Then , so and

The equation is now .

Now, let , so that .

The equation becomes , or .

Forgive me: where am I wrong?