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avatar+869 

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.

 Apr 30, 2015

Best Answer 

 #9
avatar+869 
+5

And thanks for the resized cookie

 Apr 30, 2015
 #1
avatar+95369 
+5

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

 

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     

 Apr 30, 2015
 #2
avatar+869 
0

Perfect. Here's your cookie:(Sorry, I can't find any smaller cookie )

 Apr 30, 2015
 #3
avatar+95369 
0

Thanks but I already ate far too much tonight.

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

 Apr 30, 2015
 #4
avatar+95369 
0

I was actually hoping that maybe Alan could show me how to get the other answer :/

Can you please Alan ?

 Apr 30, 2015
 #5
avatar+869 
0

I tried to shrink the image, but it appears I can't.

 Apr 30, 2015
 #6
avatar+95369 
+3

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 :)  

 Apr 30, 2015
 #7
avatar+27396 
+5

Real number solutions:

 solutions:

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

 cookie

.

 Apr 30, 2015
 #8
avatar+95369 
0

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

 Apr 30, 2015
 #9
avatar+869 
+5
Best Answer

And thanks for the resized cookie

EinsteinJr Apr 30, 2015

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