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Q4. (a) In a drive belt pulley system, the tension T newtons in the taut side is given by T = T0eμ where T0 is the tension in newtons in the slack side, μ is the coefficient of friction between the belt and pulley and θ is the angle of lap, in radians, of the belt on the pulley.

Determine EACH of the following for this system when μ = 0.25:

(i) the tension T when T₀ = 20.5 newtons and θ = 1.15 radians. (3)

(ii) the value of θ when T = 24 newtons and T₀ = 19 newtons. (5)

(b) Solve for x in EACH of the following equations:

(i) ln (1 + 3x) = - 0.63; (4)

(ii) log 5x³ – log x² = log (3x + 1). (4)