Melody

@@ End of Day Wrap    Tues 17/2/15      Sydney, Australia      Time 4:55 am      ♪ ♫

Hi all,

Today our great answers were delivered by InnovativeProgrammer, CPhill, Heureka, aliaslanturk, Geno3141, Sorasyn, NinjaDeva, Alan and Tetration.    Thanks all.    

Interest posts:   (I did not find many today)

Wed 18/2/15

divide both sides by 16

take both sides to the power of (1/4)   the answer can be positive or negative

$$\\(x^5 y^3 z)(5x^4 y^3)^2\\\\
=(x^5 y^3 z)(25x^8 y^6)\\\\
=25x^{13} y^9 z\\\\$$

solve((x/y)*x=z, (x/z)*x=y, x^2=y + z) doesnt work. i guess its a lot to handle. i was trying to experiment around the fact that (sqrt(10)/2)*sqrt(10) = 5, but if you switched 5 and 2 it still equated properly. any thoughts on the matter?

$$\\((x/y)*x=z, (x/z)*x=y, x^2=y + z)\\\\
x^2=yz\qquad x^2=y+z\\\\
y*z=y+z$$

there is an infinite number of solutions to this

The only integer solutions are y=z=0   which is not correct because you cannot divide by 0

and y=z=2      which means   x=4

Reference graph:

http://www.wolframalpha.com/input/?i=y*z%3Dy%2Bz

5'2"+5"=5'7"

I suspect that you mean     (12^[3/5]*8^[3/5]) ^5 

$$\\(12^{3/5}*8^{3/5}) ^5\\\\
12^{(3/5)*5}*8^{(3/5)*5}}\\\\
12^3*8^3}\\\\
96^3\\\$$

You can finish it  :)

Mmm  a little confusion here I think :)

$$\\ln(x)=-3\\\\
e^{ln(x)}=e^{-3}\\\\
x=e^{-3}\\\\
x=\frac{1}{e^3}$$

$$\\\frac{-113}{24} + 3\frac{ 8}{9}\\\\
-\frac{113}{24}+3\frac{ 8}{9}\\\\
-4\frac{17}{24}+ 3\frac{ 8}{9}\\\\
-4\frac{17*3}{24*3}+ 3\frac{ 8*8}{9*8}\\\\
-4\frac{51}{72}+ 3\frac{ 64}{72}\\\\
-(4\frac{51}{72}- 3\frac{ 64}{72})\\\\
-(4\frac{51}{72}- 3-\frac{ 64}{72})\\\\
-(4- 3\frac{51}{72}-\frac{ 64}{72})\\\\
-(1\frac{51}{72}-\frac{ 64}{72})\\\\
-(\frac{72+51}{72}-\frac{ 64}{72})\\\\
-(\frac{72+51-64}{72})\\\\$$

$$\\-(\frac{59}{72})\\\\
-\frac{59}{72}\\\\$$

check

$${\mathtt{\,-\,}}{\frac{{\mathtt{113}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{9}}}} = {\mathtt{\,-\,}}{\frac{{\mathtt{59}}}{{\mathtt{72}}}} = -{\mathtt{0.819\: \!444\: \!444\: \!444\: \!444\: \!4}}$$

What do you want us to do with this ?  

ans

does x(2) mean  x^2  which is     $${{\mathtt{x}}}^{{\mathtt{2}}}$$      ??