Question 1064580: Problem is:
log 0.728=x
Assume base 10.
Solve for x.
Here is how I solved this problem:
log 0.728 is equivalent to 10^x=0.728
since N is less than 1
characteristic is less than 1
so c is negative = 0+1=1 with a negative sign placed on top of 1. Thus the value of X will begin with 1.something.
That something is the mantissa obtained from appendix of a math textbook based on number 728 and mantissa is 8621.
Conclusion: x=1.8621 with a bar over digit 1 signifying it's negative number. Therefore, log0.728=x= -1.8621
CONTROVERSY:
WHEN I PLUG IN MY CALCULATOR LOG 0.728, THE ANSWER IS NOT -1.8621, BUT -0.1379. SO CALCULATOR SAYS, THE ANSWER IS -0.1379 AND MY CALCULATION SAYS THE ANSWER IS -1.8621. THE BOOK ALSO SAYS THAT THE ANSWER IS EITHER -1.8621 OR 9.8621-10=-0.1379.
COULD YOU PLEASE TELL ME WHAT DO THOSE DIFFERENT ANSWERS MEAN AND WHY ARE THEY ALL CORRECT ANSWERS? HOW CAN -1.8621 BE CORRECT AT THE SAME TIME WITH -0.1379 AND ALSO WITH 9.8621-10?
THANK YOU VERY MUCH!
Found 3 solutions by Alan3354, stanbon, josgarithmetic:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! log 0.728=x
Assume base 10.
Solve for x.
Here is how I solved this problem:
log 0.728 is equivalent to 10^x=0.728
since N is less than 1
characteristic is less than 1
so c is negative = 0+1=1 with a negative sign placed on top of 1. Thus the value of X will begin with 1.something.
That something is the mantissa obtained from appendix of a math textbook based on number 728 and mantissa is 8621.
Conclusion: x=1.8621 with a bar over digit 1 signifying it's negative number. Therefore, log0.728=x= -1.8621
CONTROVERSY:
WHEN I PLUG IN MY CALCULATOR LOG 0.728, THE ANSWER IS NOT -1.8621, BUT -0.1379. SO CALCULATOR SAYS, THE ANSWER IS -0.1379 AND MY CALCULATION SAYS THE ANSWER IS -1.8621. THE BOOK ALSO SAYS THAT THE ANSWER IS EITHER -1.8621 OR 9.8621-10=-0.1379.
COULD YOU PLEASE TELL ME WHAT DO THOSE DIFFERENT ANSWERS MEAN AND WHY ARE THEY ALL CORRECT ANSWERS? HOW CAN -1.8621 BE CORRECT AT THE SAME TIME WITH -0.1379 AND ALSO WITH 9.8621-10?
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There's no controversy.
log(0.728) = -0.1379 = 0.8621 - 1
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It was necessary to deal with the characteristic and the mantissa when using tables, but not now.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! log 0.728=x
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Using a TI-84+ I get -0.1879
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But -0.1879 = [1 + -0.1879] -1
= -1 + 0.8121
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So the characteristic is -1
and the mantissa is +0.8121
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Cheers,
Stan H.
Answer by josgarithmetic(39629) (Show Source):
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