Melody

Infinity^2 still equals infinity     :)

Thanks Einstein Jr   

If 4^x5^3x+1 = 10^2x+1, prove that x = log2 / log5

\(4^x5^{3x+1} = 10^{2x+1}\\ 2^{2x}5^{3x+1} = 5^{2x+1}*2^{2x+1}\\ 2^{2x}\div 2^{2x+1} = 5^{2x+1}\div 5^{3x+1}\\ 2^{2x-(2x+1)}= 5^{2x+1-(3x+1)}\\ 2^{-1}= 5^{-x}\\ log(2^{-1})=log( 5^{-x})\\ -log(2)=-xlog( 5)\\ \frac{log(2)}{log(5)}=x\\ x=\frac{log(2)}{log(5)} \)

can i have some too please ?

That is fine EJ,

It would just be better if you explain that in your question because otherwise a person might spend time explaining it to you and not understaning that you do not need it explained.  Maybe they would rather be do something else.   

Do you already know the answers EJ ?

Is this intended as a challenge question or do you seriously want help?

3x+7=x/2

\(3x+7=\frac{x}{2}\\ 2(3x+7)=2(\frac{x}{2})\\ 6x+14=x\\ 6x+14-x=x-x\\ 5x+14=0\\ 5x+14-14=0-14\\ 5x=-14\\ x=\frac{-14}{5}\\ x=-2\frac{4}{5}\\\)

This is MWizzard's physics question.  It is not answered yet

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(5)/(sqrt(2)-1)

\(\frac{5}{\sqrt2-1}\\ =\frac{5}{\sqrt2-1}\times \frac{\sqrt2+1}{\sqrt2+1}\\ =\frac{5(\sqrt2+1)}{(\sqrt2-1)(\sqrt2+1)}\\ =\frac{(5\sqrt2+5)}{(2-1)}\\ =5\sqrt2+5\)

you are knitting a hat, and you want it to have 3 different colored stripes. you have 6 different colors of yarn.how manydifferent hats could you knit?

I have interpreted this question in the most simple way.

How many ways can I choise 3 colours out of 6.

6C3 = nCr(6,3) = 20