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We can start by recognising one of our properties of log. That is log_a(x) - log_a(y) = log_a(x/y). Performing this on our question we get: log₃((3b+1)/(a-2)) = -1...

There is a definition which a pairing between to sets has to satisfy in order to be a function. It is like a checklist, we can go over it and tick each box to see if something is a function.

First ...

To find the maximum/minimum of a curve you must first differentiate the function and then equate it to zero. This gives you one coordinate. To find the other you must resubstitute the one already found in...

To differentiate y=(x²+4x)⁵ you need to use the chain rule. The chain rule uses the fact that dy/dx = dy/dt * dt/dx. 

Here we create a new variable t, where t = x²+...

3(3/4)x^(-1/4) which simplifies to (9/4)x^(-1/4)