SOLUTION: I need to find the value of v in the following log. v=log(base 2)(1/4) If I do as the law says, I come up with -2. But the book is showing 22. Am I doing this wrong or is t

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need to find the value of v in the following log. v=log(base 2)(1/4) If I do as the law says, I come up with -2. But the book is showing 22. Am I doing this wrong or is t      Log On

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Question 1140: I need to find the value of v in the following log.
v=log(base 2)(1/4)
If I do as the law says, I come up with -2. But the book is showing 22. Am I doing this wrong or is the books answer wrong.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
If v=log(base 2)(1/4), by definition of log,
2^v = 4.
Now if v= -2, 2^(-2) = 1/2^2 = 1/4
So your answer is correct.
One way to solve:
v = log(base 2)(1/4) = -log(base 2)4 = -log(base 2) 2^2
= - 2 log(base 2) 2 = -2 * 1 = -2.