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

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

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Rose 1 month 2021-08-17T17:58:00+00:00 1 Answer 0 views 0

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    2021-08-17T17:59:08+00:00

    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

    _______________________

    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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