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Thursday, September 20, 2012

Test Answers


Answers
Q1.   3x+2  = 45 + 4 × 3x  
Put all terms with 3x  on the left, 3x+2   – 4 × 3x    = 45
Factor out  3x  ,    3x  (3 – 4 )  = 45
…    Solve to get x = 2

Q2.     2 log5r – 3 log 125t = 2
Recall that 125 = 53, so try to get like terms on the left.  This means use the change of base formula.
2 log5r – 3 (log 5t / log 5125) = 2
2 log5r – 3 (log 5t / log 553) = 2
Next remember that log xx = 1, so log 55= 1
2 log5r – 3 (log 5t / log 553) = 2
Next the 3s will cancel
2 log5r – 3 (log 5t / 3) = 2
Replace 2 with log 5 25 and you are almost finished
…  r = 5t



















Remember AB ≠ BA



So x = 3 and y = -5 .  (Confirm by substituting into both equations).

6.    4x+2 × 2y = 8
2, 4 and 8 are related by 4 = 22 and 8 = 23.
4x+2 × 2y = 8  à(22) x+2 × 2y = 23 à 2(x+2) + y = 3  Eqn (1)
Likewise, 27x – 2  × (1/3)y = 1 à (33) x – 2  × (3) – y = 30 à Eqn (2)
Don’t forget, x0 = 1   (unless 00)
… Solve for the simultaneous equations: x = 1, y =  – 3.

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