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# Can you solve the equation:

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Can you solve the equation:

• $${{\mathtt{e}}}^{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{8}}$$

e being Euler's number, approximately 2.71828.

EinsteinJr  Apr 30, 2015

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And thanks for the resized cookie

EinsteinJr  Apr 30, 2015
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$${{\mathtt{e}}}^{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{8}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{ln}{\left({{\mathtt{13}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)}{\mathtt{\,\times\,}}{i}\right)}}{{ln}{\left({\mathtt{e}}\right)}}}\\ {\mathtt{x}} = {\frac{{ln}{\left({\mathtt{\,-\,}}\left({{\mathtt{13}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)}\right)\right)}}{{ln}{\left({\mathtt{e}}\right)}}}\\ {\mathtt{x}} = {\frac{{ln}{\left({\mathtt{\,-\,}}\left({{\mathtt{13}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)}{\mathtt{\,\times\,}}{i}\right)\right)}}{{ln}{\left({\mathtt{e}}\right)}}}\\ {\mathtt{x}} = {\frac{{ln}{\left({\mathtt{13}}\right)}}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{e}}\right)}\right)}}\\ \end{array} \right\}$$

There you go - it has got 2 real solutions and 2 imaginary solutions.

$$\\e^{4x}-5=8\\\\ e^{4x}=13\\\\ ln(e^{4x})=ln(13)\\\\ 4xln(e)=ln(13)\\\\ 4x=ln(13)\\\\ x=ln(13)/4$$

that is interesting, I missed out on one of  the answers

Melody  Apr 30, 2015
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EinsteinJr  Apr 30, 2015
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Thanks but I already ate far too much tonight.

Don't you know how to make that image smaller?

Melody  Apr 30, 2015
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I was actually hoping that maybe Alan could show me how to get the other answer :/

Melody  Apr 30, 2015
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I tried to shrink the image, but it appears I can't.

EinsteinJr  Apr 30, 2015
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Ok well thanks for the cookie I shall put it aside for later. :)

Perhaps you could find a little gold star for next time (I should be on a diet anyway)

The huge pic is a bit distracting in the middle of a thread but it was a really nice gesture :)

Melody  Apr 30, 2015
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Real number solutions:

And here's the resized cookie (copy and save for the future)!

.

Alan  Apr 30, 2015
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Thanks Alan, why didn't I think of that :)

Melody  Apr 30, 2015
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