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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

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

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    $\begingroup$ $\log (c-d) \neq \log c - \log d$ $\endgroup$ Jun 1, 2014 at 9:10
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    $\begingroup$ 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 \ $ . $\endgroup$ Jun 1, 2014 at 9:11
  • $\begingroup$ @KarolisJuodelė Thanks I just needed a confirmation. $\endgroup$
    – SA-255525
    Jun 1, 2014 at 10:36

1 Answer 1

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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)

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