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use rules: ln e^x = x*ln(e) and ln(e) = 1. find natural log of each side: (3x-9)ln(e)=ln(8). rearrange: x= (ln(8)+9)/3

Using the general complete the square formula, where x²+bx+c=0 becomes (a+b/2)²+b²+c=0, we get (x+7)²-7²-1=0 This can be rearranged to show that (x+7...

simplify: 2x^4 - 4x^(-1/2) + 3integrate each term: (2/5)x^5 - 8x^(-1/2) + 3x + c

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 4...

a)For any function y = f(g(x)) the differential will take the form dy/dx = g'(x)f'(g(x)).(This is because of the chain rule,y = f(u), u = g(x)dy/du = f'(u), du/dx = g'(x)hence dy/dx = dy/du * du/dx = g'(x...