What is the result of this expression , It should mention that the log
is natural logarithm.
$$
\log\left(\exp(-x) – \exp(-y)\right)
$$
Could we use the formula which mentioned in wikipedia about logarithmic identities?
$$
\log_{b}(a -c) = \log_b a + \log_b(1- \frac{c}{a})
$$
and does any body know the refrence of the above mentioned formula in wikipedia?
Best Answer
I assume you are familiar with $$\log r+\log s=\log(rs)$$ Now if you replace $r$ with $a$, and $s$ with $1-(c/a)$, you get $$\log a+\log(1-(c/a))=\log(a(1-(c/a)))=\log(a-c)$$ So that's the source of the identity you quote.