For any base show that
log (1+2+3)= log 1+ log 2+ log3.
Note that , in general,
log (a+b+c) $\neq$ log a+ log b +log c.

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Solution

To prove:- $log (1 + 2 + 3) = log 1 + log 2 + log 3$

Taking L.H.S.-

$log (1 + 2 + 3)$

$= log 6$

$= log (1 \times 2 \times 3)$

$= log 1 + log 2 + log 3 (∵ log a b = log a + log b)$

$=$ R.H.S.

Hence proved.

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