applying logarithm law question

Question

Here is my equation (below) on which I am applying log

$X=\frac{a}{b}\left ( c-d \right )$

so far I applied it as

$\log X=\log(a)-\log(b)+\left [ \log\left ( c \right )-\log\left ( d \right ) \right ]$

Answer 1

The equation you have given will on taking log give-

logX=log(a/b)+log(c-d)

Now as karolis commented

log(c−d)≠logc−logd log(c+d)≠logc+logd

But log(a/b) =log(a) - log(b) And loga*b=log(a) +log(b)

So we get

logX=[log(a)−log(b)]*log(c-d)