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There are numerous alternative ways to solve these simultaneous equations. For this problem, one of the simplest methods is to multiply the first equation by 3, so that we get 6x in both equations: (2x - 3y)...

The problem with this equation lies with the denominator on the left hand side. If we recall our graph of ln(x) however, we know that ln(x) is always positive and not equal to 0. Now we can safely multiply i...

Z is simply a general complex number, which can be written as Z = x+iyHere |Z-2+3i| = 1 can be written as |Z-(2-3i)| = 1, which is just an expression for every Z whose distance from the point (2,-3i) is equa...

The question says to use integration by parts on this question, but at the minute we only have one variable. Therefore, we introduce a 1, so that log|x|= 1*log|x|, here we have not altered the value of the f...

We can start by letting y = ln(x) What we are trying to show is that dy/dx = 1/x Since y = ln(x), then e y = e ln(x) = x Taking the derivative of each side of this equation will give us e y .dy/dx = 1 If we ...