Which of the following statements are correct?

$l o g (2) \times l o g (4) = l o g (4 \times 2)$

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$l o g_{3} 3 = 1$

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$l o g_{10000} 1 = 0$

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$l o g 1 + l o g 2 + l o g 3 = l o g (1 + 2 + 3)$

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Solution

The correct option is D
$l o g 1 + l o g 2 + l o g 3 = l o g (1 + 2 + 3)$

(a) Since $l o g_{b} b = 1$ , so $l o g_{3} 3 = 1$

(b) Since $l o g_{b} 1 = 0$ , so $l o g_{10000} 1 = 0$

(d) $l o g (1 + 2 + 3)$
= log 6 = log $1 \times 2 \times 3$
= log 1 + log 2 + log 3

So, option (c) is incorrect. $l o g a \times l o g b \neq l o g (a \times b)$

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