Hello atljogger Originally Posted by

**atljogger** Can someone show me how to simplify an exponential function E^x when there is a variable in the exponent? I would like to get X out of the exponent and solve for it.

$\displaystyle y =(4X+3)\frac{1}{1+e^{3X-2}}

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or more complicated

$\displaystyle y =(4X+3)\frac{1}{1+e^{3X^3+2x^2+4X-2}}

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I was able to get some help on finding the derivative in the Calculus section but have been unable to figure out how to simplify this equation.

Also, how do I calculate the square of an e^x equation:

$\displaystyle y = {(1+e^{3X-2})}^2

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The bad news is that you'll only be able to solve equations like these by numerical methods - there won't be an analytical solution. So you'll have to settle for approximate answers.

The good news is that squaring the final expression you've written down is pretty easy. Just expand in the usual way, using $\displaystyle (a+b)^2 = a^2+2ab+b^2$. So:

$\displaystyle {(1+e^{3X-2})}^2 = 1^2 + 2.1.e^{3X-2}+(e^{3X-2})^2$$\displaystyle = 1 + 2e^{3X-2}+e^{6X-4}$

Grandad