David Mackay

David Mackay commented,
Hi Mr. Knight. I see your question is 20 days old so maybe this answer is too late. I have just started helping in the Study Group after many years on KA. What you have above is two "simultaneous e...

David Mackay commented,
Thinking a bit more about it! Also worth observing that exp(x) and ln(x) are the inverse functions of each other. So we can say: exp(ln(x)) = ln(exp(x)) = x

David Mackay commented,
Also, in the equations above "ln" refers to the "natural logarithm" which is the logarithm to the base "e".

David Mackay commented,
Hi Allen. In this case I think exp(X) means "e" to the power X. Where "e" means Euler's number fully described here https://en.wikipedia.org/wiki/E_(mathematical_constant). Hope this helps!

David Mackay commented,
Probably means "exponent". But hard to say without seeing the original material. Could you post a photo of the page?

David Mackay commented,
The skill here is to carefully read the question. Then try to write down any mathematical "facts" that are stated in the question. Problems like this where you have to determine two (or more) quant...

David Mackay commented,
Hi Reyna. Sorry but you are not correct. Here is my solution: Let's use L for the number of Jill's marbles. Let's use K for the number of Jack's marbles. From the statement of the problem we can wr...

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