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(2 log(125))/(3 log(25))?

HOW DO YOU SOLVE THIS?

I know the answer is 1 but the method to solving i dont know.

anyone please help ASAP

4 Answers

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  • 9 years ago
    Favorite Answer

    (2 log(125))/(3 log(25))

    = (2 log(5^3))/(3 log(5^2))

    =(6 log(5))/(6 log(5))

    =1

  • 9 years ago

    Hint: 125 = 5³, 25 = 5²

  • 9 years ago

    i assume your log base is 10

    just punch in your calculator..

    2log125÷3log25

    and you'll get the answer

  • 9 years ago

    Before starting, you have to know that:

    Ln(a)^n = n.Ln(a)

    Ln(ab) = Ln(a) + Ln(b)

    Ln(a/b) = Ln(a) - Ln(b)

    Ln(e) = 1

    Ln(x), to be defined, x must be as: x > 0

    = [2.Ln(125)] / [3.Ln(25)]

    = [2.Ln(5)³] / [3.Ln(5)²] → you know that: Ln(a)^n = n.Ln(a)

    = [(2 * 3).Ln(5)] / [(3 * 2).Ln(5)]

    = [6.Ln(5)] / [6.Ln(5)]

    = 1

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