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To help yourself to write a clear and concise answer it can be helpful to follow the P.E.A/E.L structure when writing an essay in exams. P stands for the point you're making e.g. 'In Mary Shelly's Franken...

Laws of logs tells us that ln(a) - ln(b) = ln(a/b)

Therefore ln(10)-ln(5) = ln(10/5) = ln(2)

when differentiating, we multiply the power by the coefficient and then take the power away by 1 so : y= 4x^3 + 3x^2 -5x +1 then 4 x 3= 12 and 3-1 = 2 meaning the solution is 12x^2. 2 x 3 = 6 and 2-1 = 1 ...

Taking the log of both sides we get 5x * ln2 = (2x+1) * ln3.
Taking everything that contains x to the left side: x * (5ln2 - 2ln3) = ln3.
Therefore x=ln3/(5ln2 - 2ln3)
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It has to do with the structure of the ATP synthase protein. The part in the centre moves 120 degrees with each prototon that passes through. This makes the 3 ATP/ADP binding sites to change shape. Each o...