Question

if
$log_{2}(3) = a \: then \: the \: value \: of \: log_{2}(12) is$
​

Answer 1

Given :

$log_{2}(3) = a$

To find :

$log_{2}12$

Concept used :

$log_{b}(a \times c) = log_{b}(a) + log_{b}(c)$

$log_{a}(a) = 1$

Solution :

$log_{2}(12) = log_{2}(3 \times 4)$

$log_{2}(3 \times 4) = log_{2}(3) + log_{2}(4)$

$log_{2}(12) = log_{2}(3) + log_{2}(4)$

It is given that :-

$log_{2}(3) = a$

$log_{2}(12) = a + log_{2} {(2)}^{2}$

$log_{2}(12) = a + 2 log_{2} (2)$

now :-

$log_{2}(2) = 1$

$log_{2}(12) = a +( 2 \times 1)$

$log_{2}(12) = a +2$

Answer :

a +2

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Learn more :

$log_{b}(a \times c) = log_{b}(a) + log_{b}(c)$

$log_{b}( \frac{a}{c} ) = log_{b}(a) - log_{b}(c)$

$log_{b}( {a}^{c} ) = c \: log_{b}( {a} )$

$log_{a}(a) = 1$

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