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Math Help - Find x in this equation. I know what x is, but I don't know the steps in getting it!!

  1. #1
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    Question Find x in this equation. I know what x is, but I don't know the steps in getting it!!

    Hi all
    We have our maths exam on tuesday and I am doing revision and there is a question on this sheet we have that I can't figure out the process of answering it for.

    I have to find x, and I figured it out by guess + checking on the calculator, but how do I do it algebraically?
    4^x+3*4^x=1

    What is the steps needed to find the answer?

    Any help is appreciated
    Lachlan

    EDIT:
    Nevermind I got it ended up being something simple which I overlooked...
    I forgot that 4^x+3*4^x=4*4^x so I understood it and divided both sides by 4, and then went from there
    Last edited by auonline; August 22nd 2008 at 06:20 PM.
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  2. #2
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    To solve this, you must use logarithms. Remember some logarithm properties

    \log_a{(x \cdot y)} = \log_a{x} + \log_a{y}

    \log_a{\left(\frac{x}{y}\right)} = \log_a{x} - \log_a{y}

    \log_a{(x)^n} = n\log_a{x}

    \log_a{a} = 1

    \frac{1}{a} = a^{-1}

    ====================

    Back to your question.

    Given: 4^x + 3 * 4^x = 1

    Pull 4^x common factor: 4^x(1+3) = 1

    Divide by 4 on both sides: 4^x = \frac{1}{4} = 4^{-1}

    Take the log of base 4 on both sides: \log_4{4^x} = \log_4{4^{-1}}

    Carry down x and -1: x = -1

    Remember that \log_4{4} = 1
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  3. #3
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    Quote Originally Posted by auonline View Post
    I have to find x
    That totally cracks me up. It's right there above the four! Where were you looking?

    Seriously,

    Hint: 1*y + 3*y = 4*y
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  4. #4
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    Quote Originally Posted by TKHunny View Post
    That totally cracks me up. It's right there above the four! Where were you looking?

    Seriously,

    Hint: 1*y + 3*y = 4*y
    Lol, I remember that picture. "Here it is." Hehe
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  5. #5
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    Yeah they have that picture in our classroom too:



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  6. #6
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    Avoid Confusion: Find the value for x in the following equation...or words to that effect.
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  7. #7
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    Pythagorean Theorem

    Quote Originally Posted by auonline View Post
    Yeah they have that picture in our classroom too:



    Pythagoren Theorem states that in right triangle.doc
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  8. #8
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    Smile hehehe....try this one.

    or try this one,...my first post was non sense, i did not your question, hehehe...
    Doc3.doc
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