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?

Answer 1

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!

Answer 2

<<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.