Dados log5=0,70 e log3=0,48, calcule o valor X na equação (0,3)^x = 1,5?

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  • 0,3 = 3/10

    1,5 = 15/10

    log15/10 na base 3/10 = x

    log15/10 / log3/10 = x

    ______________________________________…

    log15/10 = log15-log10

    log15/10 = log(3.5) - 1

    log15/10 = log3+log5 - 1

    log15/10 = 0,48+0,70-1

    log15/10 = 0,18

    log3/10 = log3-log10

    log3/10 = 0,48-1

    log3/10 = -0,52

    ______________________________________…

    log15/10 / log3/10 = x

    0,18/-0,52 = x

    x = -0,34 <------------------------------

  • Oi Raquel, bom dia! Como vai?

    Dados : log5=0,70 e log3=0,48

    (0,3)^x = 1,5

    log(0,3)^x = log 1,5

    x log 0,3 = log 1,5

    x(log 0,3) = log 1,5

    x(log3/10) = log15/10

    x( log3 - log 10) = (log 3 + log5)/log10 como log10 = 1

    x(log3 -1) = log 3 + log 5

    x.0,48 -x = 0,48 + 0,70

    0,52 x = 1,18

    x = 1,18/0,52 =~2,27

  • O que seriam logs?

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