Condensing logarithmic expressions?

I'm behind in school from being sick and would really appreciate some help with this problem, I'm supposed to condense it into a single quantity:

1/3[lnx^9 - lny^12]

4 Answers

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  • 1 decade ago
    Favorite Answer

    By having a number in front of a log, you can turn it into an exponent on the variable:

    1/3(lnx^9) = lnx^9/3 = lnx^3

    1/3(lny^12) = lny^12/3 = lny^4

    Now you have:

    lnx^3 - lny^4

    When you subtract logs in the same base (here, the base is e) and want to condense the expression down to one log, you will divide. (When you are adding, you multiply):

    ln (x^3/y^4)

  • 4 years ago

    Condensing Logarithmic Expressions

  • 1 decade ago

    The exponents are brought down.

    1/3[9lnx-12lny]

    distribute

    3lnx-4lny

    when subtracting natural logarithims, divide each other

    (3/4)ln(x/y)

    This is as far as you can go!

    Hope this helps!

  • Anonymous
    1 decade ago

    (ln(x^9 / y^12) )/ 3

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