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Math Help - Common logarithims?

  1. #1
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    Common logarithims?

    Solve each equation or inequality

    Can anyone offer assistance for the following two problems

    1. 5^x=4^x+3 This is what I did
    log 5^x=log 4^x+3
    x log 5=x+3 log 4 Now I am stuck

    2. .16^4x+3= .3^8-x

    I am not entirely sure on how to start this one
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  2. #2
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    Please fix your notation. You're all over the place on that on.

    If you mean this: 5^{x} = 4^{x+3}, you should have written 5^x = 4^(x+3). Parentheses make a difference.

    This is okay, excepting the notation.

    log [5^x] = log [4^(x+3)]

    Again with notation confusion:

    x log 5 = (x+3) log 4

    Why are you stuck? Keep going!

    x log 5 = x log(4) + 3 log 4

    x log(5) - x log(4) = 3 log(4)

    x [log(5) - log(4)] = 3 log(4)

    Can you finish.

    log(4) is a number. It may not be the prettiest number ever, but it's not the ugliest, either. Use it like any other number.
    Last edited by TKHunny; May 28th 2011 at 09:44 PM.
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    For my second problem I am having some difficulty (This is what I did)

    .16^(4x+3)=.3^(8-x)

    4+3x log .16= 8-x log .3

    4 log .16 + 3x log .16= 8 log .3- x log .3

    4 log .16+3x log .16+ x log .3= 8 log .3 (I am stuck right here) Then I did this

    -3.18+(x)3 [ log .16 + log .3]= -4.183

    -3.18- 3.956x=-4.183 But I think this is wrong somehow
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  4. #4
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    Quote Originally Posted by homeylova223 View Post
    For my second problem I am having some difficulty (This is what I did)

    .16^(4x+3)=.3^(8-x)

    (4+3x) log .16= (8-x) log .3 ... parenthesis, remember?

    4 log .16 + 3x log .16= 8 log .3- x log .3

    4 log .16+3x log .16+ x log .3= 8 log .3 (I am stuck right here)

    3x log(.16) + x log(.3) = 8 log(.3) - 4 log(.16)

    factor out an x on the left side and solve.
    .
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  5. #5
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    I am still having some trouble solving it

    3x log(.16)+ x log (.3)= 8 log (.3)- log(.16)

    (x)3 log(.16)+ log(.3)=(4) log (.3)- log (.16) I multiplied 3 times log(.16) first

    -2.9105x= -1.2956
    x=.4451 But this is wrong because the answer in the back of my book says .3434

    What could I be doing wrong
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  6. #6
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    Never mind I understand now
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