book Maths Puzzle Numerical Ability

can you please provide me an explanation of why the change of base formula can be proven. I need to provide proof why this works and I am having trouble finding the answer!!! Thank you for any help you provide.

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Max Z = 5x1 + 6x2
subject to: 17x1 + 8x2 <= 136
3x1 + 4x2 <= 36
x1, x2 >= 0 and interger
What is the optimal soulition? Z =? Put the answer in the form xx with no additional nu
What quantity of 60 per cent acid solution must be mixed with a 20 per cent solution to produce 720 mL of a 50 per cent solution?