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Math Help - Log questions

  1. #1
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    Log questions

    This is for IB standard level math which is basically a review of everything through calculus and I'm having trouble remembering how to do some of this stuff. I have a test tomorrow so if anyone could help me out, it would be greatly appreciated.

    1. Solve for X and Y using a system of equations
    4^X x 8^Y = 2
    3^3X x 9^2Y = 27^(2/3)

    2. If log(base a)2 = X and log(base a)5 = Y, find...
    a. log(base 2)5
    b. log(base a)20

    3. Solve the system:
    Y = 2log(base 3)X
    Y+1 = log(base 3)9X

    4. Use the first three terms in the expansion of (1+X)^5 to find an approximate value for 1.06^5

    5. If log(base b)X = 5 and log(base b)sqrtY = 12, find...
    a. log(base b)b^Y

    I know it's not very advanced stuff but I'm having trouble with this class and I'd like to keep my GPA as high as I can until college apps are finished.

    Thanks.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Springs View Post
    This is for IB standard level math which is basically a review of everything through calculus and I'm having trouble remembering how to do some of this stuff. I have a test tomorrow so if anyone could help me out, it would be greatly appreciated.

    1. Solve for X and Y using a system of equations
    4^X x 8^Y = 2
    3^3X x 9^2Y = 27^(2/3)

    Thanks.
    4^x \cdot 8^y = 2 \Longrightarrow 2^{2x} \cdot 2^{3y}=2^1 \Longrightarrow \boxed{2x+3y=1}

    3^{3x} \cdot 9^{2y}=27^{\frac{2}{3}} \Longrightarrow 3^{3x} \cdot 3^{4y}=3^2 \Longrightarrow \boxed{3x+4y=2}

    Now solve for x and y by substitution, elimination, or matrices, whichever method you know best.
    Last edited by masters; August 24th 2008 at 04:10 PM.
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  3. #3
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    1. Solve for X and Y using a system of equations
    4^X x 8^Y = 2
    3^3X x 9^2Y = 27^(2/3)
    hints ...
    4^x = (2^2)^x
    8^y = (2^3)^y

    9^{2y} = (3^2)^{2y}
    27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}}


    2. If log(base a)2 = X and log(base a)5 = Y, find...
    a. log(base 2)5
    b. log(base a)20
    hint for part (a) ... \log_b(c) = \frac{\log_a(c)}{\log_a(b)}

    hint for part (b) ... 20 = 2^2 \cdot 5 and
    \log(b^2c) = \log(b^2) + \log(c)


    3. Solve the system:
    Y = 2log(base 3)X
    Y+1 = log(base 3)9X
    hint ... \log_3(9x) = \log_3(9) + \log_3(x)

    4. Use the first three terms in the expansion of (1+X)^5 to find an approximate value for 1.06^5
    hint ...
    (a+b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5<br />


    5. If log(base b)X = 5 and log(base b)sqrtY = 12, find...
    a. log(base b)b^Y
    hints ...
    \log_b{\sqrt{y}} = \frac{1}{2}\log_b{y}
    \log_b{b^y} = y
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