Problem with a logarithmic rule

[mrcotton]

Please could some one help me with the rules of logarithms to understand why inverting the numbers in the bracket and change the minus sign to a plus sign gives the same result?

Thank you

 

[mfb]

ln(a^b)=b*ln(a)
Try b=-1

 

[Mark44]

ln(A/B) = ln(A) - ln(B) = -[ln(B) - ln(A)] = -ln(B/A)

 

[armaant]

for the equation on the right: t= ( ln (N0/N) ) / λ:

if you multiply top and bottom of the fraction by -1 you get

t= (-1 ln (N0/N)) / -λ

You have -1 ln (N0/N) which is equal to ln( (N0/N)^-1 ) by the power rule. The (N0/N)^-1 inside the log flips to (N/N0) from the negative exponent and you get:

t= ( ln (N/N0) ) / -λ.

 

[mrcotton]

Fantastic thanks to you all