The value of loga b-log|b|= loga (b) "...

The value of `loga b-log|b|=` `loga` (b) `"log"|a|` (c) `-loga` (d) none of these

A

log a

B

`log|a|`

C

`-log a`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

log ab is defined if ` ab gt 0` or a and b have the same sign.
Case (i): a, `b gt 0`
` rArr log ab - log|b| = log a + log b - log b = log a` …(i)
Case (ii): ` a, b lt 0`
` rArr log ab - log|b| = log (-a) + log (-b) - log (-b) `
` = log (-a)` ...(ii)
From Eqs. (i) and (ii), we have
` log ab - log|b| = log |a|`.

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