Theory question 106
Logarithms(a) Simplify ½ log1025 − 2 log103 + log1018
(b) If 123y = 8310, obtain an equation in y, hence find the value of y.
(c) Solve the equation 92x−3/3x+3 = 1
Show the model answer
Model answer
(a) log 5 − log 9 + log 18 = log(5 × 18/9) = log 10 = 1.
(b) y2 + 2y + 3 = 83, so y2 + 2y − 80 = 0, (y + 10)(y − 8) = 0. y = 8 (a base must be positive and bigger than 3).
(c) 34x−6 = 3x+3, so 4x − 6 = x + 3 and x = 3.
Explanation
Write 9 as 3² so both sides have the same base.