Name: ___________________ Score: _____ / 90 MARK: ________ 22/04/2016 4 A linguistico MATHS TEST A Pass Mark: 54/90 1) (20 points) Sketch the graph of each logarithmic function by doing the following: • Sketch the asymptote and write its equation • Label at least four distinct coordinate points on each graph • Write the domain and the range • a) y = log 2
( x +1) ! 4 b) y = log 1
( x ! 2) +1 3
2) (30 points) Solve each equation: a) log ( x + 3) + log (1! x ) = 2 log 2 b) log 2 ( x + 3) + 2 log 1 ( x + 8) = 1 2
c) 2
x
! 3x"1 = 5 x"2 3)
(20 points) Solve each inequality: a) log 1
(1! x ) " !3 2
b) log
(1! x ) + log (1+ x ) > 2 log (!x ) 4) (10 points) Solve the following equation graphically: log 1 x = x + 3 2
5) (10 points) Solve the equation: log 2 log 1 ( x ! 5) = 0 3