Rearranging a Logarithm Functon

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Homework Statement



y=ae^x

Homework Equations




rearrange to find a

The Attempt at a Solution



y/a=e^x

x=ln(y/a)

x=lny-lna

lny-x=lna

now how do I rearrange/inverse to seclude a
 
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ln(y)-x = ln(a) \Rightarrow\; a = e^{ln(y)}e^{-x} = ye^{-x}
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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