# applying logarithm law 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

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

• $\log (c-d) \neq \log c - \log d$ Jun 1, 2014 at 9:10
• There is no general rule for logarithms of sums or differences of numbers: you can only write $\ \log ( \ a \pm b \ ) \$ , which has no special relation to the individual logarithms of the numbers $\ a \$ or $\ b \$ . Jun 1, 2014 at 9:11
• @KarolisJuodelė Thanks I just needed a confirmation. Jun 1, 2014 at 10:36

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)