SAT Preparation Question?
http://www.prepzel.com/questions/57
Here’s what I did:
(1/2)^5t / (1/2)^5 = 3.1^-3/(1/2)^5
(1/2)^t = 3.1^-3/(1/2)^5 = 1.07414991
Now, I’m not sure what a logarithm is, but it looked like it would work, so I did:
log 1/2 ( 1.07414991 )
and it’s not one of the choices in the question
What did I do wrong, and what’s the answer?
Need an explanation
2 Responses
Morewood
09 Feb 2010
Donald
09 Feb 2010
answer is 1.6667
did it on my calculator.
You have a very good idea: Start by getting rid of the "5".
However, your exponent laws need work!
(1/2)^(5t) / (1/2)^5 = (1/2) ^ (5t-5) is not (1/2)^t.
Instead of subtracting 5 from (5t), you need to divide, in the exponent. That means you want roots:
Fifth-root[(1/2)^(5t)] = [(1/2)^(5t)]^(1/5) = (1/2)^t
Once you have that (1/2)^t = [3.1^(-3)]^(1/5)
you other idea is fine:
Logarithm base (1/2) of {[3.1^(-3)]^(1/5)}
[Log Definition: If A^B=C, then B = Log base A of C.]
Just a small bit of weirdness, to calculate Log base A of C on most calculators, you must enter:
Log(C)/Log(A)
So your answer is: t = Log((3.1^-3)^0.2)/Log(0.5)
which is correct: calculate (1/2)^(5*t) and compare with 3.1^-3
Notice that none of the given answers on Prepzel is correct!
It appears that the question was mistyped:
Instead of 3.10^-3, it should have been 3×10^-3
(scientific notation for 0.003)