SOLUTION: How do you find the smallest power of 0.917 that yields a value less than 0.10. The answer book says 27 (rounded up). How did they get that?

Question 571283: How do you find the smallest power of 0.917 that yields a value less than 0.10. The answer book says 27 (rounded up). How did they get that?
Found 3 solutions by scott8148, unlockmath, lwsshak3:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
x log(.917) < -1
Answer by unlockmath(1688)   (Show Source): You can put this solution on YOUR website!
Hello,
Let's set this up as:
.917^x=.10
If you have a scientific calculator we can set up:
Log(.917).10=x (Note: .917 is subscript or base)
x=26.574 round this up to 27
Make sense?
RJ
www.math-unlock.com
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
How do you find the smallest power of 0.917 that yields a value less than 0.10. The answer book says 27 (rounded up). How did they get that.
**
.917^x<0.10
Take log of both sides
xlog(.917) divide both sides by log(.917) and reverse inequality signs (note: both logs<0)
x>log(0.10)/log(.917)
Using calculator
x>26.574..
The smallest power of 0.917 that yields a value less than 0.10≈27
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