There is no need to carry out the calculation. (2 ) 2. By taking logarithms of both sides, solve the equation 43p-1 = 5210 giving the value of p to one decimal place. (3) 3. (8) Given that 2 log (4- x) = log (x + 8) show that 22-9x + 8=0 (3) (b) () Write down the roots of the equation x2-9x + 8=0 (1i) State which of the roots in (b)(i) is not a solution of 2 log (4 - x) = log (x +8) giving a reason for your answer. (2) Compiled by: EBXSLC Mathematics Department 4. A car has six forward gears. The fastest speed of the car . in Jit gear is 28 km h-] . in guh gear is 115 km h-] Given that the fastest speed of the car in successive gears is modelled by an arithmetic sequence, (a) find the fastest speed of the car in 3 d gear. (3) Given that the fastest speed of the car in successive gears is modelled by a geometric sequence, (b) find the fastest speed of the car in 5th gear. (3) 5 . In the binomial expansion of (a+ 2x)2 where a is a constant the coefficient of x is 15 120 Find the value of a. (3) 6. Given that x2 +8x-3 - = Ax + B + - C xEi x*-2 x+2 x+2 find the values of the constants A, B and C (3)