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I did this maths question and got the answer -ln0.1, but the correct answer is ln10. I checked the numericals using a calculator, to find that -ln0.1 is the same as ln10. How do i convert -ln0.1 to ln10?
Answers
Answered by
jim
I don't see why you have to convert it; they are indeed the same thing. I want to draw a graph for this, but I can't :-)
In general, you can use the rule that ln(1/x) = -ln(x), so you can simply declare that and be done.
I'll try to show an equivalence so it might make a bit of sense:
ln(10) is the number you need to add in logs to multiply by 10.
ln(0.1) is the number you need to add in logs to multiply by 0.1, so -ln(0.1) is the number you need to add in logs to divide by 0.1.
But dividing by 0.1 is the same as multiplying by 10, so they're both the same number!
In general, you can use the rule that ln(1/x) = -ln(x), so you can simply declare that and be done.
I'll try to show an equivalence so it might make a bit of sense:
ln(10) is the number you need to add in logs to multiply by 10.
ln(0.1) is the number you need to add in logs to multiply by 0.1, so -ln(0.1) is the number you need to add in logs to divide by 0.1.
But dividing by 0.1 is the same as multiplying by 10, so they're both the same number!
Answered by
drwls
<<How do i convert -ln0.1 to ln10? >>
ln 0.1 = ln 1/10 = ln1 - ln10 = -ln10
Therefore -ln0.1 = ln10
Remember that the log of 1, to any base, is 0.
ln 0.1 = ln 1/10 = ln1 - ln10 = -ln10
Therefore -ln0.1 = ln10
Remember that the log of 1, to any base, is 0.
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