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find x: e^(3x-9) = 8

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
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Answered by Benjamin Y. • Maths tutor
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By completing the square, find the solutions of x which satisfy the equation x^2+14x-1=0

Using the general complete the square formula, where x 2 +bx+c=0 becomes (a+b/2) 2 +b 2 +c=0, we get (x+7) 2 -7 2 -1=0 This can be rearranged to show that (x+7) 2 =50 by taking the square root of both sides ...
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Answered by Immie F. • Maths tutor
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integrate (2x^4 - 4/sqrt(x) + 3)dx

simplify: 2x^4 - 4x^(-1/2) + 3integrate each term: (2/5)x^5 - 8x^(-1/2) + 3x + c
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Answered by Benjamin Y. • Maths tutor
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For the equation, 5(7x + 8) + 3(2x + b) ≡ ax + 13. Find the values of a and b. You may use a calculator.

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 = 41, ...
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Answered by David B. • Maths tutor
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(a) Find the differential of the the function, y = ln(sin(x)) in its simplest form and (b) find the stationary point of the curve in the range 0 < x < 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)f'...
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Answered by David B. • Maths tutor
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