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?
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!
<<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.
To convert -ln(0.1) to ln(10), let's first simplify -ln(0.1).
-ln(0.1) can be simplified using the properties of logarithms:
-ln(0.1) = -ln(1/10)
Using the logarithmic property that log(a/b) = log(a) - log(b), we can rewrite -ln(1/10) as:
-ln(1/10) = -ln(1) + ln(10)
Since ln(1) equals zero, we can simplify further:
-ln(1) + ln(10) = 0 + ln(10)
Therefore, -ln(0.1) is equal to ln(10). So, your initial answer of -ln(0.1) is indeed equivalent to ln(10). Both expressions represent the same value, just written in different forms.