SOLUTION: Hello, Problem: log16^1/2. I tried solving and I got 4. What I'm not sure of is if its negative 4 or positive? I might be completly off, but learning what i have about logari

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, Problem: log16^1/2. I tried solving and I got 4. What I'm not sure of is if its negative 4 or positive? I might be completly off, but learning what i have about logari      Log On


   

Question 242934: Hello,
Problem: log16^1/2.
I tried solving and I got 4.
What I'm not sure of is if its negative 4 or positive?
I might be completly off, but learning what i have about logarithms I think I might be on the right track.
Please let me know if its negative or positive, and my answer 4 is right.
Thanks
Found 3 solutions by jim_thompson5910, Alan3354, JimboP1977:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%2816%2C%281%2F2%29%29 Start with the given expression.


log%2810%2C%281%2F2%29%29%2Flog%2810%2C%2816%29%29 Use the change of base formula.


log%2810%2C%282%5E%28-1%29%29%29%2Flog%2810%2C%2816%29%29 Rewrite 1%2F2 as 2%5E%28-1%29


log%2810%2C%282%5E%28-1%29%29%29%2Flog%2810%2C%282%5E4%29%29 Rewrite 16 as 2%5E4


%28-1%2Alog%2810%2C%282%29%29%29%2F%284%2Alog%2810%2C%282%29%29%29 Pull down the exponents using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


%28-1%2Across%28log%2810%2C%282%29%29%29%29%2F%284%2Across%28log%2810%2C%282%29%29%29%29 Cancel out the common terms.


-1%2F4 Simplify


So log%2816%2C%281%2F2%29%29=-1%2F4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Problem: log16^1/2.
I tried solving and I got 4.
What I'm not sure of is if its negative 4 or positive?
I might be completly off, but learning what i have about logarithms I think I might be on the right track.
Please let me know if its negative or positive, and my answer 4 is right.
-------------
Check your answer.
Does 16%5E4+=+1%2F2 ?
No, 16^4 = 65536
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Does 16%5E-4+=+1%2F2 ?
No, that's 1/65536.
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16%5Elog%28x%29+=+1%2F2
16%5E%281%2F4%29+=+2
16%5E%28-1%2F4%29+=+1%2F2
so log%2816%2C1%2F2%29+=+-1%2F4

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Well you are on the right track. You cannot really solve it unless you know the base of the log. Assuming the base is say 10 you could solve this problem.
16^(1/2) is the same as saying the square root of 16 which is 4 OR -4. However log bases are always positive so you cannot take the log of -4. So it has to be the log of 4.
If the base is say 10 we are saying what power to base 10 gives 4. The answer is 0.602.
10^0.602 gives 4
Does this help at all?