Quandaries
and Queries
Who is asking: Student
Level: Secondary
Question:
My teacher wants to know why there are extraneous solutions in logarithms?
Hi Heather,
An extraneous solution might arise from the fact that the log(x) does not exist if x is negative. For example suppose you were asked to find x is
log(x) = log(x2 - 2)
A solution migh look like
log(x) = log(x2 - 2), therefore
x = x2 - 2. Hence
x2 - x - 2 = 0
(x - 2)(x + 1) = 0
Therefore x = 2 or x = -1
If you now try to verify your solution you see that x = -1 is not a solution since log(-1) does not exist. The olny solution is x = 2.
Penny