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-   -   Writing a Logarithm as a Single Term w/o a log (https://www.askmehelpdesk.com/showthread.php?t=89864)

  • May 6, 2007, 06:35 PM
    incognito
    Writing a Logarithm as a Single Term w/o a log
    Hello,
    I need help solving this problem:

    "Write 10^(log3x^2+log5x) as a single term that does not contain a logarithm"

    Now, I tried to get rid of the log's by changing everything to a common log, but that just leaves trying a 0 to as X.
    This doesn't seem right.

    Can someone please explain how to solve this problem.
    Many thanks.
  • May 7, 2007, 07:18 AM
    galactus
  • May 7, 2007, 07:18 AM
    ebaines
    Where exactly are you getting stumped? If you apply the various identities for powers and logarithms, you'll get it:

    10^(log A) = A
    log(a*b) = log(a) + log(b)
    log(a^b) = b log(a)
    10^(a+b) = 10^a * 10^b
    10^(a*b) = (10^a)^b
  • May 7, 2007, 09:59 AM
    incognito
    Quote:

    Originally Posted by galactus


    Isn't that still leaving a log term? 10^log15x^3
  • May 7, 2007, 10:05 AM
    incognito
    Quote:

    Originally Posted by ebaines
    Where exactly are you getting stumped? If you apply the various identities for powers and logarithms, you'll get it:

    10^(log A) = A
    log(a*b) = log(a) + log(b)
    log(a^b) = b log(a)
    10^(a+b) = 10^a * 10^b
    10^(a*b) = (10^a)^b


    I ended up getting 150x^3
    I multiplied the exponential logs, then used the 3rd property of logarithms to move the exponent in from of log 10, then I canceled out logs and multiplied everything together.
    Is that even possible?
  • May 7, 2007, 10:09 AM
    galactus
    Incognito, I gave you a worked out solution. 15x^3. I see no log in that. They have been eliminated

    See, . The same as if

    Oh well, I tried.
  • May 7, 2007, 02:43 PM
    incognito
    Quote:

    Originally Posted by galactus
    Incognito, I gave you a worked out solution. 15x^3. I see no log in that. They have been eliminated

    See, . The same as if

    Oh well, I tried.


    NNNOOOO WWWWAAAAAIIIITTTTT!
    Haha, my teacher only had one lecture on logarithms and the book is of no help.
    I didn't know that when you "added" logs, the log part cancels out.
    Is this a Theorem or Property?

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