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?
? asked in Science & MathematicsMathematics · 5 years ago

Can I get help on this problem please. (3/2)^x = 4^(1-x)?

3 Answers

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  • ?
    Lv 7
    5 years ago

    (3/2)^x = 4^(1 - x)

    6^x = 4

    x ≈ 0.77371

  • la console
    Lv 7
    5 years ago

    (3/2)^(x) = 4^(1 - x)

    Ln[(3/2)^(x)] = Ln[4^(1 - x)] → recall: Ln(x^a) = a.Ln(x)

    x.Ln(3/2) = (1 - x).Ln(4)

    x.Ln(3/2) = Ln(4) - x.Ln(4)

    x.Ln(3/2) + x.Ln(4) = Ln(4)

    x.[Ln(3/2) + Ln(4)] = Ln(4) → recall: Ln(a) + Ln(b) = Ln(ab)

    x.Ln(6) = Ln(4)

    x = Ln(4)/Ln(6)

  • Sqdancefan
    Lv 7
    5 years ago

    (3/2)^x = 4^(1-x)

    x*log(3/2) = (1-x)*log(4)

    x*(log(3/2)+log(4)) = log(4)

    x = log(4)/(log(3/2) +log(4))

    x = log(4)/log(6)

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