SOLUTION: What is the smallest integer value of k such that (1/2)to the power of k < 0.001?

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Question 694775: What is the smallest integer value of k such that (1/2)to the power of k < 0.001?
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is the smallest integer value of k
such that (1/2)to the power of k < 0.001?
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Solve (1/2)^k < 0.001
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Take the log of both sides:
k(log(1/2)) < log0.001
---
k < -3/log(1/2)
k < 9.9658
==============================
Ans: k = 9
===============
Cheers,
Stan H.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the smallest integer value of k such that (1/2)to the power of k < 0.001?

%281%2F2%29%5Ek+%3C+.001

log+%281%2F2%2C+.001%29+%3C+k

log+.001%2Flog+0.5+%3C+k

9.965784 < k

k > 9.965784

Since k > 9.965784, then the smallest integer value of k, is highlight_green%2810%29

You can do the check!!

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