Melody

You need to show your working Einstein :/

$$\sqrt[-1]{2}$$    I can guess at what it might mean but I have never seen an expression like this before !

I do not think that you have explained what i wrong with the logic :/

I cannot understand this question at all :/

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 :)  

sixty four

The angle is anti-clockwise from the positive x axis so that is     7pi/4

The distance out the front is from the origin so it is    $$\sqrt{4+4}=\sqrt{8}=2\sqrt2$$

so the answer is  D

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

Can you please Alan ?

Thanks but I already ate far too much tonight.

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

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

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     

10-9=1  that is the answer