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How do you evaluate $10 log 18 - log 3$ $10 log18 - log3$ ?

1 Answer

Dec 21, 2015

$10 log (18) - log (3) = log (\frac{18^{10}}{3})$ $10log(18)-log(3)=log(18^10/3)$

Explanation:

Remember

$m log (n) = log (n^{m})$ $mlog(n) = log(n^m)$
$log (a) - log (b) = log (\frac{a}{b})$ $log(a)-log(b) = log(a/b)$

Therefore
$XXX 10 log (18) - log (3)$ $color(white)("XXX")10log(18)-log(3)$

$XXX = log (18^{10}) - log (3)$ $color(white)("XXX")=log(18^10)-log(3)$

$XXX = log (\frac{18^{10}}{3})$ $color(white)("XXX")=log(18^10/3)$

This could be evaluated using a calculator as:
$XXX = 12.0756$ $color(white)("XXX")=12.0756$

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