(a). (frac{T}{sin 90^o}) = (frac{120}{sin 135^o}) and found T = 169.71N
(b) (frac{R}{sin 135^o}) = (frac{120}{sin 135^o})
R = 120N
Explanation
(a) 3 log(_2) x = y (to) 2(^y) = x(^3)………….(1)
Similarly, log(_2) 4x = y + 4 can be written as 2(^{y + 4}) = 4x…………(2)
Substituting for 2y in equation (2) to have 16x(^3) = 4x and to form a cubic equation 16x(^3) – 4x = 0.
Then, using factorizing to have 4x(4x(^2) – 1) = 0 and solving for x to get x = 0 or x = (frac{1}{2}) or (frac{1}{2})
Next, substituting for x in equation (1), when x = 0, y has no solution.
Also, when x = -(frac{1}{2}) y has no solution and when x = (frac{1}{2}), 2(^y) = ((frac{1}{2}))(^3) = 2(^{-3})
Therefore, y = -3
(b). Substitute to have -3*5 = (-3)(^2) – 2(-3) (5) + 5(^2) = 2(^n) and when simplified to get 64 = 2(^n). However, 2(^6) = 2(^n) so that n = 6.