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Thread: 3 Questions: 2 on Range and 1 on a logarithm

  1. #16
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    Re:

    Ok great thanks
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  2. #17
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    Re:

    What about the other problem on logs do you guys have any clue on that one?
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  3. #18
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    Quote Originally Posted by qbkr21 View Post

    3. When Log base b of A=2 and Log base b of D=5

    What is: Log base b of (a+d)
    $\displaystyle log_bA = 2$

    $\displaystyle log_bD = 5$

    I presume you want to know: $\displaystyle log_b(A+D)$? (Yes, case is important. A is not necessarily the same as a.)

    I couldn't tell you. With the given information I could tell you what $\displaystyle log_b(AD)$ is (its 2 + 5 = 7).

    Let me show you why this is so hard.

    $\displaystyle log_bA = 2$ means that $\displaystyle b^2 = A$. Similarly $\displaystyle log_bD = 5$ means $\displaystyle b^5 = D$. So
    $\displaystyle A + D = b^2 + b^5$

    But this is NOT a simple power of b. There IS an exponent c such that $\displaystyle b^c = b^2 + b^5$, but this is not an easy equation to solve for a general value of b, if it's even possible to do generally. (However if we know the value of b we can numerically estimate it.)

    If it still seems simple, try to find c for $\displaystyle 2^c = 2^2 + 2^5 = 4 + 32 = 36$. So $\displaystyle c = log_236 \approx 5.169925001$. But if b = 3, then $\displaystyle c = log_2252 \approx 5.033103256$.

    -Dan
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  4. #19
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    I think he wants to know,
    $\displaystyle \log_b (A\cdot D)$
    Not, $\displaystyle \log_b(A+B)$
    It seems that either he copied wrong of his teacher posed an unfair problem.
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  5. #20
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    Re:

    Dan you are right I did A time D and got 15 and that was wrong on the test. Maybe I am in way over my head, I might should have just added them. But when you expand logs through mulitiplication you add them, this is what I thought but as stated she marked it wrong. My teacher obviously wanted something totally different. Thanks Guys.
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