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Math Help - Fixing log errors.

  1. #1
    Junior Member
    Joined
    Jan 2007
    Posts
    26

    Question Fixing log errors.

    Trying to fix the log questions I got wrong. I've already fixed some, but I can't grasp these two in any way.

    1) "log(15)1"

    I did:

    log(15)1 = x
    15^x = 1
    x = 1 ------> I corrected this with 15^0 = 1 ---> x = 0. But I can't grasp/remember the rule of anything to the zero becomes one. Does zero replace x?



    2) "10^3x = 55"

    I did:

    10^3x = 55^1
    3x = 55
    x = 18.333 ---> I attempted to correct this and came up with x = log(10)55/3. I still resulted with x = 18.333 and I don't understand why this was still marked wrong.

    Thanks in advance.
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  2. #2
    Senior Member ecMathGeek's Avatar
    Joined
    Mar 2007
    Posts
    436
    Quote Originally Posted by Mulya66 View Post
    Trying to fix the log questions I got wrong. I've already fixed some, but I can't grasp these two in any way.

    1) "log(15)1"

    I did:

    log(15)1 = x
    15^x = 1
    x = 1 ------> I corrected this with 15^0 = 1 ---> x = 0. But I can't grasp/remember the rule of anything to the zero becomes one. Does zero replace x?
    log15(1) = x
    1 = 15^x

    Since we can say that 15^0 = 1, we can rewrite the problem as:
    15^0 = 15^x

    (Note that 15^0 replaced 1 in the problem 1 = 15^x, becoming 15^0 = 15^x.)

    Therefore, x = 0.

    2) "10^3x = 55"

    I did:

    10^3x = 55^1
    3x = 55
    x = 18.333 ---> I attempted to correct this and came up with x = log(10)55/3. I still resulted with x = 18.333 and I don't understand why this was still marked wrong.

    Thanks in advance.
    Is this 10^(3x) = 55 or 10^(3) * x = 55? The notation you used was a bit unclear. But I'm going to assume you mean 10^(3x) = 55.

    From this, you CANNOT say that 3x = 55. You can't set the exponent of the left hand side equal to the base of the right hand side (doing so is invalid and makes no sense). However, we can solve for x by taking the log of both sides:

    log(10^(3x)) = log(55)
    3x*log(10) = log(55)
    3x = log(55)
    x = log(55)/3

    This will be an irrational answer that you'll have to plug into your calculator to find.
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